Relevant bibliographies by topics / Commutator theory

Academic literature on the topic 'Commutator theory'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Commutator theory"

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Chekhlov, Andrey R., and Peter V. Danchev. "On commutator Krylov transitive and commutator weakly transitive Abelian p-groups." Forum Mathematicum 31, no. 6 (November 1, 2019): 1607–23. http://dx.doi.org/10.1515/forum-2019-0066.

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AbstractWe define the concepts of commutator (Krylov) transitive and strongly commutator (Krylov) transitive Abelian p-groups. These two innovations are respectively non-trivial generalizations of the notions of commutator fully transitive and strongly commutator fully transitive p-groups from a paper of Chekhlov and Danchev (J. Group Theory, 2015). They are also commutator socle-regular in the sense of Danchev and Goldsmith (J. Group Theory, 2014). Various results from there and from a paper of Goldsmith and Strüngmann (Houston J. Math., 2007) are considerably extended to this new point of view. We also define and explore the concept of a commutator weakly transitive Abelian p-group, comparing its properties with those of the aforementioned two group classes. Some affirmations, sounding quite curiously, are detected in order to illustrate the pathology of the commutators in the endomorphism rings of p-primary Abelian groups.
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FINKELSTEIN, ROBERT J. "q GAUGE THEORY." International Journal of Modern Physics A 11, no. 04 (February 10, 1996): 733–46. http://dx.doi.org/10.1142/s0217751x9600033x.

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We examine some issues that arise in the q deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields with the corresponding q commutators, the resulting propagators are not very much different from those of the undeformed theory as long as one is dealing with weak fields; but the theory still violates causality. If one postulates a q-deformed S matrix, the corresponding q causal commutator has two poles of different strength and the result again amounts to a deformation of the Lorentz group.
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Acciarri, Cristina, and Pavel Shumyatsky. "Commutators and commutator subgroups in profinite groups." Journal of Algebra 473 (March 2017): 166–82. http://dx.doi.org/10.1016/j.jalgebra.2016.11.001.

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Carro, María J. "Commutators and analytic families of operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 685–96. http://dx.doi.org/10.1017/s030821050001307x.

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This work connects the theory of commutators with analytic families of operators in abstract interpolation theory. Our main result asserts that if {Lξ}0≤Reξ≤1 is an analytic family of operators satisfying some conditions, then [Lθ,Ω] +(Lξ)′(θ): Āθ→ Bθ is bounded. From this, we can deduce the boundedness of the commutator .
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Kaushik, Rahul, and Manoj K. Yadav. "Commutators and commutator subgroups of finite p-groups." Journal of Algebra 568 (February 2021): 314–48. http://dx.doi.org/10.1016/j.jalgebra.2020.10.007.

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Stanovský, David, and Petr Vojtěchovský. "Commutator theory for loops." Journal of Algebra 399 (February 2014): 290–322. http://dx.doi.org/10.1016/j.jalgebra.2013.08.045.

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Faizal, Mir. "Deformation of second and third quantization." International Journal of Modern Physics A 30, no. 09 (March 25, 2015): 1550036. http://dx.doi.org/10.1142/s0217751x15500360.

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In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler–DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.
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Lipparini, Paolo. "Commutator theory without join-distributivity." Transactions of the American Mathematical Society 346, no. 1 (January 1, 1994): 177–202. http://dx.doi.org/10.1090/s0002-9947-1994-1257643-7.

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Robinson, Derek W. "Commutator Theory on Hilbert Space." Canadian Journal of Mathematics 39, no. 5 (October 1, 1987): 1235–80. http://dx.doi.org/10.4153/cjm-1987-063-2.

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Commutator theory has its origins in constructive quantum field theory. It was initially developed by Glirnm and Jaffe [7] as a method to establish self-adjointness of quantum fields and model Hamiltonians. But it has subsequently proved useful for a variety of other problems in field theory [17] [15] [8] [3], quantum mechanics [5], and Lie group theory [6]. Despite all these detailed applications no attempt appears to have been made to systematically develop the theory although reviews have been given in [22] and [9]. The primary aim of the present paper is to partially correct this situation. The secondary aim is to apply the theory to the analysis of first and second order partial differential operators associated with a Lie group.
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Pedicchio, M. C. "Arithmetical categories and commutator theory." Applied Categorical Structures 4, no. 2-3 (1996): 297–305. http://dx.doi.org/10.1007/bf00122258.

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Dissertations / Theses on the topic "Commutator theory"

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edu, wodzicki@math berkeley. "Commutator Structure of Operator Ideals." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1062.ps.

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Liu, Zhi Kang. "Some norm inequalities of the commutator for even-order tensors." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691384.

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Lok, Io Kei. "Norm inequalities for a matrix product analogous to the commutator." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182886.

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DI, MICCO DAVIDE. "AN INTRINSIC APPROACH TO THE NON-ABELIAN TENSOR PRODUCT." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/703934.

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The notion of a non-abelian tensor product of groups first appeared in a paper where Brown and Loday generalised a theorem on CW-complexes by using the new notion of non-abelian tensor product of two groups acting on each other, instead of the usual tensor product of abelian groups. In particular, they took two groups acting on each other and they defined their non-abelian tensor product via an explicit presentation. This led to the development of an algebraic theory based on this construction. Many results were obtained treating the properties which are satisfied by this non-abelian tensor product as well as some explicit calculations in particular classes of groups. In order to state many of their results regarding this tensor product, Brown and Loday needed to require, as an additional condition, that the two groups M and N acted on each other compatibly: these amount to the existence of a group L and of two crossed modules structures of M and N on L such that the original actions are induced from these crossed module structures. Furthermore, they proved that the non-abelian tensor product is part of a so-called crossed square of groups: this particular crossed square is the pushout of a specific diagram in the category of crossed squares of groups. Note that crossed squares are a 2-dimensional version of crossed modules of groups. Following the idea of generalising the algebraic theory arising from the study of the non-abelian tensor product of groups, Ellis gave a definition of non-abelian tensor product of Lie algebras, and obtained similar results. Further generalisations have been studied in the contexts of Leibniz algebras, restricted Lie algebras, Lie-Rinehart algebras, Hom-Lie algebras, Hom-Leibniz algebras, Hom-Lie-Rinehart algebras, Lie superalgebras and restricted Lie superalgebras. The aim of our work is to build a general version of non-abelian tensor product, having the specific definitions in the categories of groups and Lie algebras as particular instances. In order to do so we first extend the concept of a pair of compatible actions (introduced in the case of groups by Brown and Loday and in the case of Lie algebras by Ellis) to semi-abelian categories. This is indeed the most general environment in which we are able to talk about actions, due to the concept of internal actions. In this general context, we give a diagrammatic definition of the compatibility conditions for internal actions, which specialises to the particular definitions known for groups and Lie algebras. We then give a new construction of the Peiffer product in this setting and we use these tools to show that in any semi-abelian category satisfying the "Smith-is-Huq" condition, asking that two actions are compatible is the same as requiring that these actions are induced from a pair of internal crossed modules over a common base object. Thanks to this equivalence, in order to deal with the generalisation to the semi-abelian context of the non-abelian tensor product, we are able to use a pair of internal crossed modules over a common base object instead of a pair of compatible internal actions, whose formalism is far more intricate. Now we fix a semi-abelian category A satisfying "Smith-is-Huq" and we show that, for each pair of internal L-crossed modules, it is possible to construct an internal crossed square which is the pushout (in the category of crossed squares) of the general version of the diagram used by Brown and Loday in the groups case. The non-abelian tensor product is then defined as a piece of this internal crossed square. We show that if A is the category of groups or the category of Lie algebras, this general construction coincides with the specific notions of non-abelian tensor products already known in these settings. We construct an L-crossed module structure on this non-abelian tensor product, some additional universal properties are shown and by using these we prove that this tensor product is a bifunctor. Once we have the non-abelian tensor product among our tools, we are also able to state the new definition of "weak crossed square": the idea behind this is to generalise the explicit presentations of crossed squares known for groups and for Lie algebras. These equivalent definitions, which (contrarily to the semi-abelian one) do not rely on the formalism of internal groupoids but include some set-theoretic constructions, are shown to be equivalent to the implicit ones, where, by definition, crossed squares are crossed modules of crossed modules and hence normalisations of double groupoids. Our idea is to give an alternative explicit description of crossed squares of groups (resp. Lie algebras) using the non-abelian tensor product, so that it does not involve anymore the so-called emph{crossed pairing} (resp. emph{Lie pairing}), which is not a morphism in the base category but only a set-theoretic function; in its place we use a morphism from the non-abelian tensor product which is more suitable for generalisations. Doing so, the explicit definitions can be summarised by saying that a crossed square is a commutative square of crossed modules, compatible with an additional crossed module structure on the diagonal, and endowed with a morphism out of the non-abelian tensor product. Our definition of weak crossed squares is based on the one of non-abelian tensor product and plays the role of the explicit version of the definition of internal crossed squares: in particular we proved that it restricts to the explicit definitions for groups and Lie algebras and hence that in these cases weak crossed squares are equivalent to crossed squares. So far we have shown that any internal crossed square is automatically a weak crossed square, but we are currently missing precise conditions on the base category under which the converse is true: this means that any internal crossed square can be described explicitly as a particular weak crossed square, but this is not a complete characterisation. In order to give a direct application of our non-abelian tensor product construction, we focus on universal central extensions in the category of L-crossed modules: Casas and Van der Linden studied the theory of universal central extensions in semi-abelian categories, using the general notion of central extension (with respect to a Birkhoff subcategory) given by Janelidze and Kelly. We are mainly interested in one of their results, namely that, given a Birkhoff subcategory B of a semi-abelian category X with enough projectives, an object of X is B-perfect if and only if it admits a universal B-central extension. Edalatzadeh considered the category of L-crossed modules of Lie algebras and crossed modules with vanishing aspherical commutator as Birkhoff subcategory B. Since the first one is not a semi-abelian category the existing theory does not apply in this situation: nevertheless he managed to prove the same result, and furthermore he gave an explicit construction of the universal B-central extensions by using the non-abelian tensor product of Lie algebras. Using our general definition of non-abelian tensor product of L-crossed modules as given in the third chapter, we are able to extend Edalatzadeh's results to the category of L-crossed modules in any semi-abelian category A satisfying the "Smith-is-Huq" condition: this is a useful application of the construction of the non-abelian tensor product, which again manages to express in this more general setting exactly the same properties as in its known particular instances. Furthermore, taking the subcategory of abelian objects as Birkhoff subcategory of the category of crossed modules in A, we are able to show that, whenever the category A has enough projectives, our generalisation of Edalatzadeh's work is partly a consequence of Casas' and Van der Linden's theorem, reframing Edalatzadeh's result within the standard theory of universal central extensions in the semi-abelian context. There are two non-trivial consequences of this fact. First of all, besides the existence of the universal B-central extension for each B-perfect crossed module in A, we are also able to give its explicit construction by using the non-abelian tensor product: notice that this construction is completely unrelated to what has been done by Casas and Van der Linden. Secondly, this construction of universal B-central extensions is valid even when A does not have enough projectives, whereas within the general theory this is a key requirement for the result to hold.
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Rogers, Duncan M. "Anomalous commutators and the BJL limit." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26525.

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The BJL limit is derived and used to calculate the anomalous vector current commutator in QED. It is then shown, by a calculation with the BJL limit for double commutators, that the Jacobi identity fails for two vector currents and one axial vector current in QED.
Science, Faculty of
Physics and Astronomy, Department of
Graduate
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Fong, Kin Sio. "Norm inequalities for commutators." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182877.

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Mandich, Marc Adrien. "Commutators, spectral analysis, and applications to discrete Schrödinger operators." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0725/document.

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L’objet de cette thèse est l’étude spectrale et dynamique de systèmes de la mécanique quantique en utilisant des techniques de commutateurs. Deux parmi les trois articles présentés traitent l’opérateur de Schrödinger discret sur un réseau. Dans le premier article, un principe d’absorption limite est établi pour le Laplacien discret multidimensionnel perturbé par la somme d’un potentiel de type Wigner-von Neumann et d’un potentiel de type longue portée. Ce résultat implique notamment l’absolue continuité du spectre de cet Hamiltonien à certaines énergies. Dans le second article, nous considérons à nouveau l’opérateur de Schrödinger discret multidimensionnel dont le potentiel est de type longue portée. Il est démontré que les fonctions propres correspondant à des valeurs propres de l’Hamiltonien décroissent sous-exponentiellement lorsque ces dernières ne sont pas un seuil. En dimension un, il est démontré de surcroît que ces fonctions propres décroissent exponentiellement. Une conséquence de ceci est l’absence de valeurs propres dans la partie centrale du spectre délimité aux extrémités par des seuils. Le troisième article étudie des propriétés dynamiques d’Hamiltoniens vérifiant des hypothèses minimales dans la théorie des commutateurs. En se basant sur une estimation des vitesses minimales d’une part et une version améliorée du théorème du RAGE d’autre part, nous dérivons deux estimations de propagation pour cette famille d’Hamiltoniens. Ces estimations indiquent que les états du système se comportent dynamiquement de façon très similaire aux états de diffusion. Toutefois, ceci n’écarte pas la possibilité de spectre singulier continu
This thesis deals with the analysis of spectral and dynamical properties of quantum mechanical systems using techniques of operator commutators. Two of the three research papers that are presented deal exclusively with the discrete Schrödinger operators on the lattice. The first article proves a limiting absorption principle for the multi-dimensional discrete Laplacian perturbed by the sum of a Wigner-von Neumann potential and long-range potential. This result notably implies the absolute continuity of the spectrum of this Hamiltonian at certain energies. The second article proves that eigenfunctions corresponding to non-threshold eigenvalues of multidimensional discrete Schrödinger operators decay sub-exponentially. In one dimension, it is further proven that these eigenfunctions decay exponentially. A consequence of this is the absence of eigenvalues when the middle portion of the spectrum does not contain any thresholds. The third article investigates dynamical properties of Hamiltonians under very minimal assumptions in the theory of commutators. Based on minimal escape velocities and an improved version of the RAGE Theorem, we derive propagation estimates for these types of Hamiltonians. These estimates indicate that the states of the system behave dynamically very much like scattering states. Nonetheless, the existence of singularly continuous states cannot be disproved
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Hamdi, Tarek. "Calcul stochastique commutatif et non-commutatif : théorie et application." Thesis, Besançon, 2013. http://www.theses.fr/2013BESA2015/document.

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Mon travail de thèse est composé de deux parties bien distinctes, la première partie est consacrée à l’analysestochastique en temps discret des marches aléatoires obtuses quant à la deuxième partie, elle est liée aux probabili-tés libres. Dans la première partie, on donne une construction des intégrales stochastiques itérées par rapport à unefamille de martingales normales d-dimentionelles. Celle-ci permet d’étudier la propriété de représentation chaotiqueen temps discret et mène à une construction des opérateurs gradient et divergence sur les chaos de Wiener correspon-dant. [...] d’une EDP non linéaire alors que la deuxième est de nature combinatoire.Dans un second temps, on a revisité la description de la mesure spectrale de la partie radiale du mouvement Browniensur Gl(d,C) quand d ! +¥. Biane a démontré que cette mesure est absolument continue par rapport à la mesurede Lebesgue et que son support est compact dans R+. Notre contribution consiste à redémontrer le résultat de Bianeen partant d’une représentation intégrale de la suite des moments sur une courbe de Jordon autour de l’origine etmoyennant des outils simples de l’analyse réelle et complexe
My PhD work is composed of two parts, the first part is dedicated to the discrete-time stochastic analysis for obtuse random walks as to the second part, it is linked to free probability. In the first part, we present a construction of the stochastic integral of predictable square-integrable processes and the associated multiple stochastic integrals ofsymmetric functions on Nn (n_1), with respect to a normal martingale.[...] In a second step, we revisited thedescription of the marginal distribution of the Brownian motion on the large-size complex linear group. Precisely, let (Z(d)t )t_0 be a Brownian motion on GL(d,C) and consider nt the limit as d !¥ of the distribution of (Z(d)t/d)⋆Z(d)t/d with respect to E×tr
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Lefrançois, M. "Theories des champs topologiques et mecanique quantique en espace non-commutatif." Phd thesis, Université Claude Bernard - Lyon I, 2005. http://tel.archives-ouvertes.fr/tel-00012196.

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Le Modèle Standard de la physique des particules décrit les interactions entre les constituants élémentaires de la matière. Cependant, il ne parvient pas à concilier théorie quantique des champs et relativité générale. Cette thèse se focalise sur deux approches au-delà du Modèle Standard, a priori différentes mais non nécessairement
incompatibles entre elles : les théories des champs topologiques et la mécanique quantique en espace non-commutatif.
Les théories topologiques ont été introduites par Witten il y a une vingtaine d'années et possèdent un lien très étroit avec les mathématiques : leurs observables
sont des invariants topologiques de la variété d'espace-temps étudiée. Dans ce mémoire, nous nous intéressons en premier lieu à une théorie de Yang-Mills topologique. Ce modèle-jouet est ici abordé dans
un formalisme de superespace et nous dégageons une méthode systématique de détermination de ses observables. L'intérêt est double : d'une part,
retrouver les résultats obtenus précédemment dans une jauge particulière (de Wess et Zumino) et d'autre part, calculer les observables dans une superjauge quelconque. Notre approche a ainsi permis de vérifier que les observables découvertes jusque là en théorie de
Yang-Mills topologique étaient les seules possibles. Le formalisme développé peut ensuite être appliqué à des
modèles plus complexes; dans cette optique, nous détaillons ici le cas de la gravité topologique.
La mécanique quantique en espace non-commutatif propose une extension de l'algèbre de Heisenberg
de la mécanique quantique ordinaire. La différence tient au fait que les différentes composantes des opérateurs position ou moment ne commutent plus entre elles. Par conséquent, il est nécessaire de renoncer à la notion de point en introduisant une «longueur fondamentale». Nous nous intéressons dans la deuxième partie de ce
manuscrit à la description des différentes algèbres de
commutateurs rencontrées. Des applications à des systèmes quantiques en dimension deux (système de Landau, oscillateur harmonique,...) ainsi qu'une généralisation au cas de systèmes supersymétriques sont présentées.
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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Books on the topic "Commutator theory"

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Freese, Ralph. Commutator theory for congruence modular varieties. Cambridge: Cambridge University Press, 1987.

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Freese, Ralph S. Commutator theory for congruence modular varieties. Cambridge [Cambridgeshire]: Cambridge University Press, 1987.

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Boutet de Monvel-Berthier, Anne, 1948- and Georgescu V. 1947-, eds. C₀-groups, commutator methods, and spectral theory of N-Body Hamiltonians. Basel: Birkhäuser Verlag, 1996.

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Amrein, Werner O., Anne Boutet de Monvel, and Vladimir Georgescu. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Basel: Springer Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-0733-3.

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Amrein, Werner O., Anne Boutet Monvel, and Vladimir Georgescu. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-7762-6.

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Boutet, Monvel Anne, and Georgescu Vladimir, eds. C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians. Basel: Birkhäuser Basel, 1996.

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Kalton, Nigel J. Nonlinear commutators in interpolation theory. Providence, R.I., USA: American Mathematical Society, 1988.

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Bru, J. B., and W. de Siqueira Pedra. Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-45784-0.

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Lázár, J. Park-vector theory of line-commutated three-phase bridge converters. Budapest: OMIKK, 1987.

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Modern digital design and switching theory. Boca Raton: CRC Press, 1992.

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Book chapters on the topic "Commutator theory"

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Mantovani, Sandra, and Andrea Montoli. "Categorical Commutator Theory." In New Perspectives in Algebra, Topology and Categories, 147–72. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-84319-9_5.

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Clement, Anthony E., Stephen Majewicz, and Marcos Zyman. "Commutator Calculus." In The Theory of Nilpotent Groups, 1–21. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66213-8_1.

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Maher, Philip J. "Commutator Approximants." In Operator Approximant Problems Arising from Quantum Theory, 27–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61170-9_4.

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Wenzel, David. "Dominating the Commutator." In Topics in Operator Theory, 579–600. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0158-0_35.

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Herbst, Ira, and Thomas L. Kriete. "The Howland–Kato Commutator Problem." In Analysis and Operator Theory, 191–223. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12661-2_10.

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N. Mordeson, John, Kiran R. Bhutani, and Azriel Rosenfeld. "Nilpotent, Commutator, and Solvable Fuzzy Subgroups." In Fuzzy Group Theory, 61–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/10936443_3.

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Adachi, Tadayoshi, Kyohei Itakura, Kenichi Ito, and Erik Skibsted. "Commutator Methods for N-Body Schrödinger Operators." In Spectral Theory and Mathematical Physics, 1–15. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55556-6_1.

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Celledoni, E. "Eulerian and semi-Lagrangian schemes based on commutator-free exponential integrators." In Group Theory and Numerical Analysis, 77–90. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/crmp/039/06.

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Amrein, Werner O., Anne Boutet Monvel, and Vladimir Georgescu. "Spectral Theory of N-Body Hamiltonians." In C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, 401–32. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-7762-6_9.

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Amrein, Werner O., Anne Boutet Monvel, and V. Georgescu. "Spectral Theory of N-Body Hamiltonians." In C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, 401–32. Basel: Springer Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-0733-3_9.

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Conference papers on the topic "Commutator theory"

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Snell, Antony. "A Unified Method for Modeling 3 Phase Synchronous Machines." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12483.

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The use of 3 phase synchronous machines (motor or generator) is becoming more widespread with the introduction of variable frequency drives, which allow the machines to be used very effectively as low maintenance alternatives to brushed DC commutator motors. However, mathematical modeling of these machines is often difficult to understand. Many textbooks on electro-mechanical machines introduce the synchronous machine using a phasor model of the voltages induced in the armature and the applied voltage. This yields some neat results of output torque as a function of the torque angle but fails to provide much insight into how this torque comes about. Furthermore, the method assumes that the resistance of the armature windings is negligible compared with armature reactance. The method falls apart when resistance must be included. Even when armature resistance is small, there is no insight into how efficiency is compromised by copper losses in the armature. The approach described in this paper is based on the same theory, which is usually used to explain the operation of DC commutator machines. This approach provides direct insight into how torque is developed. Losses introduced by armature resistance are included so reasonable efficiency estimates can be made. Meanwhile the neat results of the simple phasor model can be obtained as a special cases by setting armature resistance to zero.
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2

Bergou, J., and M. Hillery. "Pump statistics and photon statistics in the micromaser." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.fnn4.

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The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.
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3

Snell, Antony. "A Unified Method of Modeling a 3-Phase Induction Motors." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12482.

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Many textbooks on electro-mechanical machines introduce the induction motor using a transformer circuit model connected to a fictitious load resistor, the value of which changes as a function of the slip speed. The method is essentially a power based analysis, which yields some neat, quick results. The developed torque is calculated in terms of the power developed in that fictitious resistor. Although clever in its simplicity, the method fails to provide much physical insight into how the developed torque comes about. One is just expected to trust the circuit model. The approach described in this paper is based on theory of Lorentz force and Faraday’s Law used successfully to explain the operation of DC commutator machines. The method is readily understood and it provides direct insight into how the torque is developed. The paper will introduce a torque angle, which can be useful in visualizing how the machines work. It will also be shown that the traditional transformer model of the motor can be derived from the new analysis.
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4

Chaichian, M. "Quantum field theory on noncommutative space-time and its implication on spin-statistics theorem." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337731.

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5

Mojahedie, Mohammad, and Marek Osinski. "Effects of operator ordering in effective-mass Hamiltonian on transition energies in semiconductor quantum wells." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.wh4.

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It has been recognized that use of the effective mass theory for abrupt interfaces between different materials suffers from ambiguity in kinetic- energy operator ordering, caused by nonvanishing commutator of the momentum operator and the position-dependent effective mass. This leads to nonuniqueness of the Hamiltonian, which in its general form can be written as a one-parameter family of operators.1 The matching conditions for the envelope wave function and its derivative at the interfaces are also parametrized.1 Recently, Fu and Chao reported2 that experimentally observable interband transition energies are not sensitive to the effective- mass operator ordering. In this paper, we demonstrate that optical transition energies do vary substantially with ordering. Specifically, we have analyzed GaAs/AlGaAs quantum wells using the transfer matrix technique.2 We have investigated the effects of quantum well parameters, such as subband index, thicknesses of both constituent materials, and barrier height (composition) on the shifts of subband-edge energy, between the two extreme cases of operator ordering. Calculated energy levels are more sensitive to ordering for higher subbands and for decreasing well thickness. Increasing the barrier height or thickness in coupled quantum wells will also result in a larger shift of subband-edge energies. Comparison with available data allows us to choose the ordering that provides the best fit to experiment.
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Mishra, A. K. "Quantum field theory for orthofermions and orthobosons." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337726.

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7

Berry, Michael. "Quantum indistinguishability: Spin-statistics without relativity or field theory?" In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337708.

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Hilborn, Robert C. "Connecting q-mutator theory with experimental tests of the spin-statistics connection." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337722.

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9

Salynsky, Sergey. "Quantum theory, canonical commutation relations." In The XIXth International Workshop on High Energy Physics and Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.104.0047.

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10

Sudarshan, E. C. G. "Rotational invariance, the spin-statistics connection and the TCP theorem." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337711.

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Reports on the topic "Commutator theory"

1

McCune, W. A case study in automated theorem proving: A difficult problem about commutators. Office of Scientific and Technical Information (OSTI), February 1995. http://dx.doi.org/10.2172/27057.

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2

Boyle, M., and Elizabeth Rico. Terrestrial vegetation monitoring at Cumberland Island National Seashore: 2020 data summary. National Park Service, September 2022. http://dx.doi.org/10.36967/2294287.

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The Southeast Coast Network (SECN) conducts long-term terrestrial vegetation monitoring as part of the nationwide Inventory and Monitoring Program of the National Park Service (NPS). The vegetation community vital sign is one of the primary-tier resources identified by SECN park managers, and it is currently conducted at 15 network parks (DeVivo et al. 2008). Monitoring plants and their associated communities over time allows for targeted understanding of ecosystems within the SECN geography, which provides managers information about the degree of change within their parks’ natural vegetation. 2020 marks the first year of conducting this monitoring effort at Cumberland Island National Seashore (CUIS). Fifty-six vegetation plots were established throughout the park from May through July. Data collected in each plot included species richness across multiple spatial scales, species-specific cover and constancy, species-specific woody stem seedling/sapling counts and adult tree (greater than 10 centimeters [3.9 inches {in}]) diameter at breast height (DBH), overall tree health, landform, soil, observed disturbance, and woody biomass (i.e., fuel load) estimates. This report summarizes the baseline (year 1) terrestrial vegetation data collected at Cumberland Island National Seashore in 2020. Data were stratified across three dominant broadly defined habitats within the park, including Coastal Plain Upland Open Woodlands, Maritime Open Upland Grasslands, and Maritime Upland Forests and Shrublands. Noteworthy findings include: 213 vascular plant taxa (species or lower) were observed across 56 vegetation plots, including 12 species not previously documented within the park. The most frequently encountered species in each broadly defined habitat included: Coastal Plain Upland Open Woodlands: longleaf + pond pine (Pinus palustris; P. serotina), redbay (Persea borbonia), saw palmetto (Serenoa repens), wax-myrtle (Morella cerifera), deerberry (Vaccinium stamineum), variable panicgrass (Dichanthelium commutatum), and hemlock rosette grass (Dichanthelium portoricense). Maritime Open Upland Grasslands: wax-myrtle, saw greenbrier (Smilax auriculata), sea oats (Uniola paniculata), and other forbs and graminoids. Maritime Upland Forests and Shrublands: live oak (Quercus virginiana), redbay, saw palmetto, muscadine (Muscadinia rotundifolia), and Spanish moss (Tillandsia usneoides) Two non-native species, Chinaberry (Melia azedarach) and bahiagrass (Paspalum notatum), categorized as invasive by the Georgia Exotic Pest Plant Council (GA-EPPC 2018) were encountered in four different Maritime Upland Forest and Shrubland plots during this monitoring effort. Six vascular plant species listed as rare and tracked by the Georgia Department of Natural Resources (GADNR 2022) were observed in these monitoring plots, including the state listed “Rare” Florida swampprivet (Forestiera segregata var. segregata) and sandywoods sedge (Carex dasycarpa) and the “Unusual” green fly orchid (Epidendrum conopseum). Longleaf and pond pine were the most dominant species within the tree stratum of Coastal Plain Upland Open Woodland habitat types; live oak was the most dominant species of Maritime Upland Forest and Shrubland types. Saw palmetto and rusty staggerbush (Lyonia ferruginea) dominated the sapling stratum within Maritime Upland Forest and Shrubland habitat types. Of the 20 tree-sized redbay trees measured during this monitoring effort only three were living and these were observed with severely declining vigor, indicating the prevalence and recent historical impact of laurel wilt disease (LWD) across the island’s maritime forest ecosystems. There was an unexpectedly low abundance of sweet grass (Muhlenbergia sericea) and saltmeadow cordgrass (Spartina patens) within interdune swale plots of Maritime Open Upland habitats on the island, which could be a result of grazing activity by feral horses. Live oak is the dominant tree-sized species across...
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