Relevant bibliographies by topics / Weyle invariance

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Weyle invariance'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Weyle invariance"

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NIETO, J. A. "REMARKS ON WEYL INVARIANT p-BRANES AND Dp-BRANES." Modern Physics Letters A 16, no. 40 (December 28, 2001): 2567–78. http://dx.doi.org/10.1142/s0217732301005497.

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A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity–dilaton effective action in higher dimensions, we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes.
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Edery, Ariel, and Yu Nakayama. "Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance." Modern Physics Letters A 30, no. 30 (September 7, 2015): 1550152. http://dx.doi.org/10.1142/s0217732315501527.

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Recently, it has been pointed out that dimensionless actions in four-dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein–Hilbert action with cosmological constant and a Higgs mass. The model also contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling [Formula: see text] between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the Standard Model can be incorporated into the original restricted Weyl invariant action.
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Futorny, Vyacheslav, and João Schwarz. "Holonomic modules for rings of invariant differential operators." International Journal of Algebra and Computation 31, no. 04 (April 10, 2021): 605–22. http://dx.doi.org/10.1142/s0218196721500296.

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We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1.
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SUZUKI, HIROSHI. "THERMAL PARTITION FUNCTION OF NON-CRITICAL BOSONIC STRINGS." Modern Physics Letters A 04, no. 21 (October 20, 1989): 2085–92. http://dx.doi.org/10.1142/s0217732389002343.

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The thermal free energy of free non-critical bosonic strings in a D-dimensional spacetime is examined. By integrating (or summing) over the Weyl freedom, the free energy and the one-loop vacuum amplitude are modular invariant for any D<26. Thus the (background) Weyl invariance is realized. In the case of L→∞, where L is the compactification radius of the Weyl mode, the physical spectrum circulating in the loop becomes continuous. A connection between this continuous spectrum and the unitarity of string perturbation theory is briefly mentioned.
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JAIN, SANJAY. "CONFORMALLY INVARIANT FIELD THEORY IN TWO DIMENSIONS AND STRINGS IN CURVED SPACETIME." International Journal of Modern Physics A 03, no. 08 (August 1988): 1759–846. http://dx.doi.org/10.1142/s0217751x8800076x.

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The formalism of conformally invariant field theory on a 2-dimensional real manifold with an intrinsic metric is developed in the functional integral framework. This formalism is used to study the relationships between reparametrization, Weyl, conformal and BRST invariances for strings in generic backgrounds. Conformal invariance of string amplitudes in the presence of backgrounds is formulated in terms of the Virasoro conditions, i.e., that physical vertex operators generate (1,1) representations of the Virasoro algebra, or, equivalently, the condition Q|Ψ〉=0 on physical states |Ψ〉, where Q is the BRST charge. The consequences of these conditions are investigated in the case of specific backgrounds. Strings in group manifolds are discussed exactly. For a generic slowly varying spacetime metric and dilaton field, a perturbatively renormalized vertex operator solution to the Virasoro conditions is constructed. It is shown that the existence of a solution to the Virasoro conditions or the equation Q|Ψ〉=0 requires the spacetime metric to satisfy Einstein’s equations. These conditions therefore constitute equations of motion for both the spectrum and backgrounds of string theory.
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CHO, Y. M. "MONOPOLE CONDENSATION AND MASS GAP IN SU(3) QCD." International Journal of Modern Physics A 29, no. 03n04 (February 10, 2014): 1450013. http://dx.doi.org/10.1142/s0217751x14500134.

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We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.
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ZENKIN, S. V. "GENERAL FORM OF THE LATTICE FERMION ACTION." Modern Physics Letters A 06, no. 02 (January 20, 1991): 151–55. http://dx.doi.org/10.1142/s0217732391000105.

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A set of lattice fermion actions is found which are consistent with canonical quantization of fermion systems. A new type of non-local chirally invariant action determined by the Weyl quantization is found to be inconsistent with gauge invariance. This completes the demonstration of the inconsistency of the non-local actions. The other actions are of the generalized Wilson form and may have the Kogut-Susskind-like symmetry which forbids mass terms.
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IRAC-ASTAUD, MICHÈLE. "DIFFERENTIAL CALCULUS ON A THREE-PARAMETER OSCILLATOR ALGEBRA." Reviews in Mathematical Physics 08, no. 08 (November 1996): 1083–90. http://dx.doi.org/10.1142/s0129055x96000408.

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Two differential calculi are developed on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a ten-generator Hopf algebra. We discuss the special case where it reduces to a deformation of the invariance group of the Weyl-Heisenberg algebra for which we prove the existence of a constraint between the values of the parameters.
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HARADA, KOJI. "EQUIVALENCE BETWEEN THE WESS-ZUMINO-WITTEN MODEL AND TWO CHIRAL BOSONS." International Journal of Modern Physics A 06, no. 19 (August 10, 1991): 3399–418. http://dx.doi.org/10.1142/s0217751x91001659.

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We establish the formal equivalence of a bosonized Dirac fermion (the Wess-Zumino-Witten model) to two bosonized Weyl fermions (Sonnenschein’s chiral bosons) in the path integral framework. These two systems can be regarded as gauge-fixed systems of the same gauge-invariant theory. Factorization of the fermion determinant of QCD2 is naturally realized in terms of chiral bosonization, up to a contact term which is necessary for maintaining gauge invariance. Canonical quantization of the gauge-invariantly extended system is performed.
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Temme, Francis P. "Commutator-Based (A)[X]n(SU(2)×Sn) NMR Cluster Systems: Establishment of the Universality of [n](Sn) Salients and Constraints on ϕ±11(1.1) Polarisations to the [1n] Salient: Permutational Spin Symmetry (PSS) Within NMR Spin Dynamics - an Analytic View." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1177–95. http://dx.doi.org/10.1135/cccc20051177.

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Analytic SU(2) × Sn dual tensorial (DT) spin dynamics over uniform NMR spins is invoked in examining the modern quantum basis for the universal non-observability rule which governs dominant intracluster JXX' couplings of (A)[X]n NMR systems as a specific form of (abstract) permutational spin symmetry (PSS) with well defined properties on spin-alone space. This is shown to be linked to DT constraints that apply to the cross-product ϕ1±1(1.1) polarisation development i.e., as being confined to [1n](Sn) (Liouvillian) salient, with the existence of [n] (rotating frame) null subspaces. Both these arise within the spin dynamics of (A)[X]2 spin systems (or subsystems thereof) within (a hierarchy of) dominant JXX' governing the internal L(0); such spin systems provide analytic sequels to comparative spin dynamics studies of XX' PSS and AX broken-PSS systems in a Liouvillian coupled tensorial basis formalism, since both draw on (Sanctuary B. C.: Mol. Phys. 1985, 55, 1017), and on the realisation that proper PSS over a (uniform) spin-space L(0) = [H(0),.] zeroth-order Liouvillian and its internal (hierarchical subsets of) JXX' (Temme F. P.: J. Mol. Struct. (THEOCHEM) 2002, 547, 153) i.e., for abstract Sn ↓ G group embeddings. The present work also examines the general irrep-structure of DT spin symmetries for the extent of unit-character irreps and the role of Sn ⊃ Sn-1 ⊃ .. ⊃ [2](S2) group chains in defining the Sn multiple invariants under democratic recoupling of PSS of uniform spin systems. As group measures, these properties apply to both (A)[X]n and [AX]n PSS symmetries, with the invariant cardinality |SI|(n) being related to time-reversal invariance (TRI) and its inherent democratic recoupling (DR) over Weyl (I • I) pairs. For [X]2n uniform spin clusters, |SI|(2n) is best derived via n-fold polyhedral combinatorics of the underlying DR (Temme F. P.: Proc. R. Soc. London, Ser. A 2005, 461, 321) i.e., as an augmented post-Weyl view of the essential role of TRI in (group) invariant cardinality, with the Sn-invariants represented by certain Sn subduction properties.
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Dissertations / Theses on the topic "Weyle invariance"

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Bonezzi, Roberto <1983&gt. "Complex higher spins, Weyl invariance and tractors." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amsdottorato.unibo.it/3546/1/bonezzi_roberto_tesi.pdf.

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In this thesis work I analyze higher spin field theories from a first quantized perspective, finding in particular new equations describing complex higher spin fields on Kaehler manifolds. They are studied by means of worldline path integrals and canonical quantization, in the framework of supersymmetric spinning particle theories, in order to investigate their quantum properties both in flat and curved backgrounds. For instance, by quantizing a spinning particle with one complex extended supersymmetry, I describe quantum massless (p,0)-forms and find a worldline representation for their effective action on a Kaehler background, as well as exact duality relations. Interesting results are found also in the definition of the functional integral for the so called O(N) spinning particles, that will allow to study real higher spins on curved spaces. In the second part, I study Weyl invariant field theories by using a particular mathematical framework known as tractor calculus, that enable to maintain at each step manifest Weyl covariance.
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Bonezzi, Roberto <1983&gt. "Complex higher spins, Weyl invariance and tractors." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amsdottorato.unibo.it/3546/.

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In this thesis work I analyze higher spin field theories from a first quantized perspective, finding in particular new equations describing complex higher spin fields on Kaehler manifolds. They are studied by means of worldline path integrals and canonical quantization, in the framework of supersymmetric spinning particle theories, in order to investigate their quantum properties both in flat and curved backgrounds. For instance, by quantizing a spinning particle with one complex extended supersymmetry, I describe quantum massless (p,0)-forms and find a worldline representation for their effective action on a Kaehler background, as well as exact duality relations. Interesting results are found also in the definition of the functional integral for the so called O(N) spinning particles, that will allow to study real higher spins on curved spaces. In the second part, I study Weyl invariant field theories by using a particular mathematical framework known as tractor calculus, that enable to maintain at each step manifest Weyl covariance.
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Wang, Haowu. "Reflective modular forms and Weyl invariant E8 Jacobi modular forms." Thesis, Lille 1, 2019. http://www.theses.fr/2019LIL1I028/document.

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Cette thèse comprend deux parties indépendantes. Dans la première partie, nous développons une approche fondée sur la théorie des formes de Jacobi dont l'indice est un réseau pour classifier les formes modulaires réflexives sur des réseaux de niveau arbitraire. Les formes modulaires réflexives ont des applications en géométrie algébrique, en algèbre de Lie et en arithmétique. La classification des formes modulaires réflexives est un problème ouvert et a été étudiée par Borcherds, Gritsenko, Nikulin, Scheithauer et Ma depuis 1998. Dans cette partie, nous établissons de nouvelles conditions nécessaires à l'existence d'une forme modulaire réflexive. Nous prouvons la non-existence de formes modulaires réflexives et de formes modulaires 2-réflexives sur des réseaux de grand rang. Nous donnons également une classification complète des formes modulaires 2-réflexives sur des réseaux contenant deux plans hyperboliques.La deuxième partie est consacrée à l’étude des formes de Jacobi de $W(E_8)$-invariantes. Ce type de formes de Jacobi a une signification dans les variétés de Frobenius, la théorie de Gromov-Witten et la théorie des cordes. En 1992, Wirthm\"{u}ller a prouvé que l’espace des formes de Jacobi pour tout système de racines irréductible excepté $E_8$ est une algèbre polynomiale. Très peu de choses sont connues dans le cas de $E_8$. Dans cette partie, nous montrons que l'anneau bigradué des formes de Jacobi $W(E_8)$-invariantes n'est pas une algèbre polynomiale et prouvons que chacune de ces formes de Jacobi peut être exprimée uniquement sous la forme d'un polynôme en neuf formes de Jacobi algébriquement indépendantes introduites par Sakai avec des coefficients méromorphes $\SL_2(\ZZ)$-modulaires. Ce dernier résultat implique que, à indice fixé, l’espace des formes de Jacobi $W(E_8)$-invariantes est un module libre sur l’anneau des formes $\SL_2(\ZZ)$-modulaires et que le nombre de générateurs peut être calculé via une série génératrice. Nous déterminons et construisons tous les générateurs pour des indices petits. Ces résultats étendent un théorème de type de Chevalley au cas du réseau $E_8$
This thesis consists of two independent parts. In the first part we develop an approach based on the theory of Jacobi forms of lattice index to classify reflective modular forms on lattices of arbitrary level. Reflective modular forms have applications in algebraic geometry, Lie algebra and arithmetic. The classification of reflective modular forms is an open problem and has been investigated by Borcherds, Gritsenko, Nikulin, Scheithauer and Ma since 1998. In this part, we establish new necessary conditions for the existence of a reflective modular form. We prove non-existence of reflective modular forms and 2-reflective modular forms on lattices of large rank. We also give a complete classification of 2-reflective modular forms on lattices containing two hyperbolic planes. The second part is devoted to the study of Weyl invariant $E_8$ Jacobi forms. This type of Jacobi forms has significance in Frobenius manifolds, Gromov--Witten theory and string theory. In 1992, Wirthm\"{u}ller proved that the space of Jacobi forms for any irreducible root system not of type $E_8$ is a polynomial algebra. But very little has been known about the case of $E_8$. In this paper we show that the bigraded ring of Weyl invariant $E_8$ Jacobi forms is not a polynomial algebra and prove that every such Jacobi form can be expressed uniquely as a polynomial in nine algebraically independent Jacobi forms introduced by Sakai with coefficients which are meromorphic $\SL_2(\ZZ)$ modular forms. The latter result implies that the space of Weyl invariant $E_8$ Jacobi forms of fixed index is a free module over the ring of $\SL_2(\ZZ)$ modular forms and that the number of generators can be calculated by a generating series. We determine and construct all generators of small index. These results give a proper extension of the Chevalley type theorem to the case of $E_8$
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Davies, Ian James. "A large-D Weyl invariant string model in Anti-de Sitter space." Thesis, Durham University, 2002. http://etheses.dur.ac.uk/3838/.

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In this thesis we present a novel scheme for calculating the bosonic string partition function on certain curved backgrounds related to Anti-de Sitter [AdS] space. We take the concept of a large expansion from nonlinear sigma models in particle physics and apply it to the bosonic string theory sigma model, where the analogous large dimensionless parameter is the dimension of the target space, D. We then perform a perturbative expansion in negative powers of D, rather than in positive powers of α/ι(^2)(the conventional expansion parameter).As a specific example of a curved geometry of interest, we focus on an example of the metric proposed by Polyakov [1] to describe the dynamics of the Wilson loop of pure SU(N) Yang-Mills theory, namely AdS space. Using heat kernel methods, we find that within the large-D scheme one can obtain different conditions for Weyl invariance than those found in [2]. This is because our scheme is valid for backgrounds where a is no longer small. In particular, we find that it is possible to have a dilaton that depends on the holographic coordinate only, provided one allows mixing of the ghost and matter sectors of the worldsheet theory. This field preserves Poincare invariance in the gauge theory, unlike the conventional dilaton. We also compute a simple string amplitude by constructing certain vertex operators for a scalar field in AdS, and discuss the consequences for the string spectrum.
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Eckes, Christophe. "Groupes, invariants et géométries dans l'œuvre de Weyl : Une étude des écrits de Hermann Weyl en mathématiques, physique mathématique et philosophie, 1910-1931." Thesis, Lyon 3, 2011. http://www.theses.fr/2011LYO30069/document.

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Nous entendons confronter pratique des mathématiques et réflexions sur les mathématiques dans l'œuvre de Weyl. Nous étudierons : (a) ses monographies en analyse complexe, en relativité générale et en mécanique quantique, (b) les articles en lien avec ces ouvrages, (c) certains de ses cours, (d) sa correspondance avec divers scientifiques, principalement A. Einstein, E. Cartan, J. von Neumann. Nous voulons savoir si les théories mathématiques qu'il investit conditionnent ses positions sur les fondements des mathématiques. Inversement, nous montrerons que les philosophies auxquelles il se réfère – essentiellement le criticisme kantien, l'idéalisme fichtéen et la phénoménologie de Husserl – conditionnent ses recherches. Tout d'abord, nous reviendrons sur Die Idee der Riemannschen Fläche (première éd. 1913). Nous montrerons qu'il opte alors pour un formalisme mitigé. Il se revendique de deux traditions incarnées par Klein et par Hilbert. Ensuite, nous étudierons les éditions successives de Raum, Zeit, Materie (1918-1923). Nous aborderons le projet d'une géométrie purement infinitésimale qui permet à Weyl de proposer une théorie unifiée des champs, cette dernière étant réfutée par Einstein, Pauli, Reichenbach, Hilbert and Eddington. Nous décrirons aussi la construction et la résolution de son « problème de l'espace » (1921-1923). Nous indiquerons comment la référence aux philosophies de Fichte et de Husserl permet d'éclairer ces deux projets. Enfin, nous commenterons l'article de Weyl sur les groupes de Lie (1925-1926) ainsi que son ouvrage Gruppentheorie und Quantenmechanik (1928, 1931). Son article sur les groupes de Lie manifeste la voie moyenne entre formalisme et intuitionnisme qu'il adopte en 1924. Son ouvrage en mécanique quantique incarne quant à lui un « tournant empirique » dans son épistémologie qu'il conviendra de comparer \`a l'« empirisme logique »
Our purpose consists in comparing Weyl's mathematical practice with his philosophical reflections on mathematics. We will study (a) his monographs on complex analysis, general relativity and quantum mechanics, (b) the articles which are linked to these books, (c) some of his lecture courses, (d) his correspondence with different scientists, mainly A. Einstein, E. Cartan, J. von Neumann. We will show that his mathematical research has a strong influence on the different stands he successively takes regarding the foundations of mathematics. Conversely, we will show that the philosophical systems he refers to (mainly kantian criticism, fichtean idealism and husserlian phenomenology) have a real impact on his investigations in mathematics. We will first analyse Die Idee der Riemannschen Fläche (first edition 1913). In this book, Weyl seems to take up a formalist point of view, but this is partly true. In fact, he is influenced by two traditions respectively embodied by Hilbert and Klein. Then, we will study the successive editions of Raum, Zeit, Materie (1918-1923). We will describe Weyl's project of a “purely infinitesimal geometry”. Thanks to this geometrical framework, he builds a unified fields theory, which will be disproved by Einstein, Pauli, Reichenbach, Hilbert and Eddington. During this short period, Weyl also constructs and solves the so-called space problem (1921-1923). Weyl's references to Fichte and Husserl have a significant impact on these two projects. Finally, we will comment Weyl's main article on Lie groups (1925-1926) and his monograph on quantum mechanics, i.e. Gruppentheorie und Quantenmechanik (1rst ed. 1928, 2nd ed. 1931). Weyl's article on Lie groups is in accordance with his compromise between intuitionism and formalism (1924). On the other hand, Weyl's book on quantum mechanics encapsulates an “empirical turn” in his epistemology, which will be compared with the so-called empirical logicism
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Hill, David Edward. "The Jantzen-Shapovalov form and Cartan invariants of symmetric groups and Hecke algebras /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959351&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2007.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 107-108). Also available for download via the World Wide Web; free to University of Oregon users.
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Broccoli, Matteo. "On the trace anomaly of a Weyl fermion in a gauge background." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16408/.

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In this thesis we study the trace anomaly of a Weyl fermion in an abelian gauge background. We first introduce the topic of anomaly in Quantum Fields Theory and provide case studies of a global and a gauge anomaly. Then, we review the lagrangians of the Weyl fermion and Dirac fermion, the models that are the focus of our chiral and trace anomaly computations. Since we evaluate the anomalies using Pauli-Villars (PV) regularization, we present different PV masses and discuss the classical symmetries they break. We identify the differential operators that enter our regularization schemes and we review the method that we use to evaluate anomalies: we read them from the path integral à la Fujikawa and compute them with heat kernel formulas. Then, we evaluate the chiral and trace anomaly of the models we are interested in. The chiral anomaly is well studied in the literature and we reproduce the standard result. The trace anomaly is our original result and, although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. The issue is analogous to the one recently discussed in the literature about a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds. With an abelian gauge background, this odd-parity term would be a Chern-Pontryagin density, that does not appear in our final results.
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Reho, Riccardo. "A higher derivative fermion model." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/19852/.

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Nel presente elaborato studiamo un modello fermionico libero ed invariante di scala con derivate di ordine elevato. In particolare, controlliamo che la simmetria di scala sia estendibile all'intero gruppo conforme. Essendoci derivate di ordine più alto il modello non è unitario, ma costituisce un nuovo esempio di teoria conforme libera. Nelle prime sezioni riguardiamo la teoria generale del bosone libero, partendo dapprima con modelli semplici con derivate di ordine basso, per poi estenderci a dimensioni arbitrarie e derivate più alte. In questo modo illustriamo la tecnica che ci permette di ottenere un modello conforme da un modello invariante di scala, attraverso l'accoppiamento con la gravità e richiedendo l'ulteriore invarianza di Weyl. Se questo è possibile, il modello originale ammette certamente l'intera simmetria conforme, che emerge come generata dai vettori di Killing conformi. Nel modello scalare l'accoppiamento con la gravità necessita di nuovi termini nell'azione, indispensabili anche la teoria sia appunto invariante di Weyl. La costruzione di questi nuovi termini viene ripetuta per un particolare modello fermionico, con azione contenente l'operatore di Dirac al cubo, per il quale dimostriamo l'invarianza conforme. Tale modello descrive equazioni del moto con derivate al terzo ordine. Dal momento che l'invarianza di Weyl garantisce anche l'invarianza conforme, ci si aspetta che il tensore energia-impulso corrispondente sia a traccia nulla. Per ogni modello introdotto controlliamo sistematicamente che tale condizione sia verifiata, ed in particolar modo per il caso della teoria fermionica con operator di Dirac cubico, che rappresenta il contributo originale di questa tesi.
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Hezard, David. "Sur le support unipotent des faisceaux-caractères." Phd thesis, Université Claude Bernard - Lyon I, 2004. http://tel.archives-ouvertes.fr/tel-00012071.

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Soit G un groupe algébrique réductif connexe de centre connexe défini sur un corps fini de caractéristique p>0. On munit cette structure d'un endomorphisme de Frobenius F et l'on note G^F l'ensemble des points de G fixes pour l'action de F : G^F est un groupe fini. On suppose que la caractéristique p est bonne pour G.

On définit alors une application Phi_G de l'ensemble des classes de conjugaison spéciales de G^* dans l'ensemble des classes unipotentes de G. Cette application décrit le support unipotent des différentes classes de faisceaux-caractères définis sur G.

Parallèlement à cela, via la correspondance de Springer, on définit différents invariants, dont les d-invariants, pour les caractères d'un groupe de Weyl W. Nous avons étudié le lien entre l'induction de caractères spéciaux de certains sous groupes de W et les d-invariants. A l'aide de ceci, on démontre que Phi_G, restreinte à certaines classes spéciales particulières de G^* est surjective. On a montré que la stabilité vis-à-vis du Frobenius pouvait être introduite dans ce résultat.

On en déduit deux résultats. Le premier est un lien étroit entre les restrictions aux éléments unipotents de faisceaux-caractères de certaines classes et différents systèmes locaux irréductibles et G-équivariants sur les classes unipotentes de G.

Le second est une preuve d'une conjecture de Kawanaka sur les caractères de Gelfand-Graev généralisés de G : ils forment une base du Z-module des caractères virtuels de G^F à support unipotent.
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Körber, Martin Julius. "Phase-Space Localization of Chaotic Resonance States due to Partial Transport Barriers." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-218817.

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Classical partial transport barriers govern both classical and quantum dynamics of generic Hamiltonian systems. Chaotic eigenstates of quantum systems are known to localize on either side of a partial barrier if the flux connecting the two sides is not resolved by means of Heisenberg's uncertainty. Surprisingly, in open systems, in which orbits can escape, chaotic resonance states exhibit such a localization even if the flux across the partial barrier is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states. Moreover, we show that the number of long-lived chaotic resonance states that localize on one particular side of the partial barrier is described by an individual fractal Weyl law. For a generic phase space, this implies a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of phase space.
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Books on the topic "Weyle invariance"

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Strocchi, Franco. Gauge Invariance and Weyl-polymer Quantization. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6.

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Strocchi, Franco. Gauge Invariance and Weyl-polymer Quantization. Springer, 2015.

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Strocchi, Franco. Gauge Invariance and Weyl-Polymer Quantization. Springer London, Limited, 2015.

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Rajeev, S. G. Boundary Layers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0007.

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It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’s equations to one dimension. They can then be solved numerically. A convergent analytic approximation was also found by H. Weyl. The drag on a flat plate can now be derived, resolving d’Alembert’s paradox. When the boundary is too long, Prandtl’s theory breaks down: the boundary layer becomes turbulent or separates from the wall.
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Book chapters on the topic "Weyle invariance"

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Helgason, Sigurdur. "Invariant Differential Operators and Weyl Group Invariants." In Progress in Mathematics, 193–200. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0455-8_9.

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Strocchi, Franco. "Heisenberg Quantization and Weyl Quantization." In Gauge Invariance and Weyl-polymer Quantization, 1–9. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_1.

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Strocchi, Franco. "Diffeomorphism Invariance and Weyl Polymer Quantization." In Gauge Invariance and Weyl-polymer Quantization, 77–84. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_5.

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Strocchi, Franco. "Delocalization, Gauge Invariance and Non-regular Representations." In Gauge Invariance and Weyl-polymer Quantization, 11–33. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_2.

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Strocchi, Franco. "Quantum Mechanical Gauge Models." In Gauge Invariance and Weyl-polymer Quantization, 35–51. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_3.

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Strocchi, Franco. "Non-regular Representations in Quantum Field Theory." In Gauge Invariance and Weyl-polymer Quantization, 53–76. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_4.

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Strocchi, Franco. "∗ A Generalization of the Stone-von Neumann Theorem." In Gauge Invariance and Weyl-polymer Quantization, 85–90. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-17695-6_6.

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Ryckman, Thomas. "Hermann Weyl and “First Philosophy”: Constituting Gauge Invariance." In The Western Ontario Series In Philosophy of Science, 279–98. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-9510-8_17.

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Shi, Jian-Yi. "Left cells are characterized by the generalized right τ-invariant." In The Kazhdan-Lusztig Cells in Certain Affine Weyl Groups, 236–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0074984.

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Bertrand, J., and M. Irac-Astaud. "Invariant Differential Calculus on a Deformation of the Weyl-Heisenberg Algebra." In Modern Group Theoretical Methods in Physics, 37–49. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8543-9_4.

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Conference papers on the topic "Weyle invariance"

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Jackiw, R. "Weyl Invariant Dynamics in 3 Dimensions." In PARTICLES, STRINGS, AND COSMOLOGY: 11th International Symposium on Particles, Strings, and Cosmology; PASCOS 2005. AIP, 2005. http://dx.doi.org/10.1063/1.2149712.

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Oda, Ichiro. "Planck scale from broken local conformal invariance in Weyl geometry." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Trieste, Italy: Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0070.

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NAKATA, Fuminori. "S1-INVARIANT EINSTEIN-WEYL STRUCTURE AND TWISTOR CORRESPONDENCE." In 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0003.

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Fishman, Louis. "Direct and Inverse Wave Propagation in the Frequency Domain via the Weyl Operator Symbol Calculus." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0660.

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Abstract Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The equations for the reflection and transmission operators are first-order in range, nonlinear (Riccati-like), and, in general, nonlocal. The singularity structure of the corresponding Weyl operator symbols plays a crucial role in the development of both direct and inverse wave propagation algorithms.
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