Articles de revues : « Integrable quantum field theories »

1

Fioretto, Davide, et Giuseppe Mussardo. « Quantum quenches in integrable field theories ». New Journal of Physics 12, n^o 5 (28 mai 2010) : 055015. http://dx.doi.org/10.1088/1367-2630/12/5/055015.

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BOSTELMANN, HENNING, GANDALF LECHNER et GERARDO MORSELLA. « SCALING LIMITS OF INTEGRABLE QUANTUM FIELD THEORIES ». Reviews in Mathematical Physics 23, n^o 10 (novembre 2011) : 1115–56. http://dx.doi.org/10.1142/s0129055x11004539.

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Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the Möbius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.

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MARSHAKOV, A. « EXACT SOLUTIONS TO QUANTUM FIELD THEORIES AND INTEGRABLE EQUATIONS ». Modern Physics Letters A 11, n^o 14 (10 mai 1996) : 1169–83. http://dx.doi.org/10.1142/s021773239600120x.

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The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular we consider in detail several examples of the appearance of solutions to the first-order integrable equations of hydrodynamical type and stress that all known examples can be treated as partial solutions to the same problem in the theory of integrable systems.

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Miramontes, J. Luis, et C. R. Fernández-Pousa. « Integrable quantum field theories with unstable particles ». Physics Letters B 472, n^o 3-4 (janvier 2000) : 392–401. http://dx.doi.org/10.1016/s0370-2693(99)01444-6.

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Smirnov, F. A., et A. B. Zamolodchikov. « On space of integrable quantum field theories ». Nuclear Physics B 915 (février 2017) : 363–83. http://dx.doi.org/10.1016/j.nuclphysb.2016.12.014.

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Delfino, G., G. Mussardo et P. Simonetti. « Non-integrable quantum field theories as perturbations of certain integrable models ». Nuclear Physics B 473, n^o 3 (août 1996) : 469–508. http://dx.doi.org/10.1016/0550-3213(96)00265-9.

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Bostelmann, H., et D. Cadamuro. « An operator expansion for integrable quantum field theories ». Journal of Physics A : Mathematical and Theoretical 46, n^o 9 (15 février 2013) : 095401. http://dx.doi.org/10.1088/1751-8113/46/9/095401.

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Balog, J., M. Niedermaier, F. Niedermayer, A. Patrascioiu, E. Seiler et P. Weisz. « The intrinsic coupling in integrable quantum field theories ». Nuclear Physics B 583, n^o 3 (septembre 2000) : 614–70. http://dx.doi.org/10.1016/s0550-3213(00)00277-7.

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Mathur, Samir D. « Quantum Kac-Moody symmetry in integrable field theories ». Nuclear Physics B 369, n^o 1-2 (janvier 1992) : 433–60. http://dx.doi.org/10.1016/0550-3213(92)90393-p.

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Lechner, Gandalf. « Deformations of Quantum Field Theories and Integrable Models ». Communications in Mathematical Physics 312, n^o 1 (3 décembre 2011) : 265–302. http://dx.doi.org/10.1007/s00220-011-1390-y.

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GORSKY, A., et K. SELIVANOV. « THRESHOLD AMPLITUDES IN FIELD THEORIES AND INTEGRABLE SYSTEMS ». Modern Physics Letters A 11, n^o 19 (21 juin 1996) : 1597–604. http://dx.doi.org/10.1142/s0217732396001594.

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We discuss the threshold tree amplitudes in different nonintegrable quantum field theories in the framework of integrability. The amplitudes are related to some Baker functions defined on the auxiliary spectral curves and the nullification phenomena are shown to allow a topological interpretation.

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COKER, DAVID A. « USE OF PROJECTORS FOR INTEGRABLE MODELS OF QUANTUM FIELD THEORY ». International Journal of Modern Physics B 06, n^o 17 (10 septembre 1992) : 2893–911. http://dx.doi.org/10.1142/s0217979292002292.

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This paper is a discussion of the placement of integrable field theory models on a lattice of arbitrary spacing and the construction of the corresponding quantum integrals of motion. Two methods for producing local lattice models of both fundamental and nonfundamental types are covered. It is shown how projectors can be used to construct quasilocal lattice integrable models from quantum integrable field theories. The advantage of the projector method over other methods is the preservation of the original [Formula: see text]-matrix. The integrable structure of the model is then left unchanged and the continuum integrals of motion are regained in the infinitesimal lattice limit.

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Yagi, Junya. « Branes and integrable lattice models ». Modern Physics Letters A 32, n^o 03 (11 janvier 2017) : 1730003. http://dx.doi.org/10.1142/s0217732317300038.

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This is a brief review of my work on the correspondence between four-dimensional [Formula: see text] supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.

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CASTRO-ALVAREDO, O. A., et A. FRING. « APPLICATIONS OF QUANTUM INTEGRABLE SYSTEMS ». International Journal of Modern Physics A 19, supp02 (mai 2004) : 92–116. http://dx.doi.org/10.1142/s0217751x04020336.

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We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demonstrating that the emission spectrum of a minimally coupled laser field of frequency ω to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, by evaluating expressions for the conductance in the high temperature regime we show that multiples of the characteristic filling fractions of the Jain sequence, which occur in the fractional quantum Hall effect, can be obtained from quantum wires which are described by minimal affine Toda field theories.

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15

Saleur, Hubert, et Birgit Wehefritz-Kaufmann. « Integrable quantum field theories with OSP(m/2n) symmetries ». Nuclear Physics B 628, n^o 3 (mai 2002) : 407–41. http://dx.doi.org/10.1016/s0550-3213(02)00092-5.

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Niedermaier, Max. « Varying the Unruh temperature in integrable quantum field theories ». Nuclear Physics B 535, n^o 3 (décembre 1998) : 621–49. http://dx.doi.org/10.1016/s0550-3213(98)00685-3.

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Bostelmann, Henning, et Daniela Cadamuro. « Characterization of Local Observables in Integrable Quantum Field Theories ». Communications in Mathematical Physics 337, n^o 3 (27 février 2015) : 1199–240. http://dx.doi.org/10.1007/s00220-015-2294-z.

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Alazzawi, Sabina. « Deformations of Fermionic Quantum Field Theories and Integrable Models ». Letters in Mathematical Physics 103, n^o 1 (22 juin 2012) : 37–58. http://dx.doi.org/10.1007/s11005-012-0576-3.

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19

Smit, Dirk-Jan. « A quantum group structure in integrable conformal field theories ». Communications in Mathematical Physics 128, n^o 1 (mars 1990) : 1–37. http://dx.doi.org/10.1007/bf02097043.

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Marshakov, A. « Lecture on SUSY Gauge Theories and Integrable Systems ». International Journal of Modern Physics B 11, n^o 26n27 (30 octobre 1997) : 3093–124. http://dx.doi.org/10.1142/s0217979297001519.

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I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

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21

De VEGA, H. J. « YANG-BAXTER ALGEBRAS, INTEGRABLE THEORIES AND QUANTUM GROUPS ». International Journal of Modern Physics A 04, n^o 10 (juin 1989) : 2371–463. http://dx.doi.org/10.1142/s0217751x89000959.

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The Yang-Baxter-Zamolodchikov-Faddeev (YBZF) algebras and their many applications are the subject of this reivew. I start by the solvable lattice statistical models constructed from YBZF algebras. All two-dimensional integrable vertex models follow in this way and are solvable via Bethe Ansatz (BA) and their generalizations. The six-vertex model solution and its q(2q−1) vertex generalization including its nested BA construction are exposed. YBZF algebras and their associated physical models are classified in terms of simple Lie algebras. It is shown how these lattice models yield both solvable massive quantum field theories (QFT) and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. The method of finite-size calculations from the BA is described as well as its applications to derive the conformal properties of integrable lattice models. It is conjectured that all integrable QFT and conformal models follow in a scaling limit from these YBZF algebras. A discussion on braid and quantum groups concludes this review.

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22

MUSSARDO, GIUSEPPE. « INTEGRABLE DEFORMATIONS OF CONFORMAL THEORIES AND BOOTSTRAP TREES ». International Journal of Modern Physics B 06, n^o 11n12 (juin 1992) : 2061–74. http://dx.doi.org/10.1142/s0217979292001018.

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Recent results in the study of massive integrable quantum field theories in (1+1) dimensions considered as perturbed conformal minimal models are presented. The on mass-shell properties of such theories, with a particular emphasis on the bootstrap principle, are investigated.

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23

Mussardo, G. « On the finite temperature formalism in integrable quantum field theories ». Journal of Physics A : Mathematical and General 34, n^o 36 (3 septembre 2001) : 7399–410. http://dx.doi.org/10.1088/0305-4470/34/36/319.

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24

Essler, Fabian H. L., et Robert M. Konik. « Finite-temperature dynamical correlations in massive integrable quantum field theories ». Journal of Statistical Mechanics : Theory and Experiment 2009, n^o 09 (30 septembre 2009) : P09018. http://dx.doi.org/10.1088/1742-5468/2009/09/p09018.

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Sotiriadis, S., D. Fioretto et G. Mussardo. « Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories ». Journal of Statistical Mechanics : Theory and Experiment 2012, n^o 02 (27 février 2012) : P02017. http://dx.doi.org/10.1088/1742-5468/2012/02/p02017.

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26

Castro-Alvaredo, Olalla, et Andreas Fring. « On vacuum energies and renomalizability in integrable quantum field theories ». Nuclear Physics B 687, n^o 3 (mai 2004) : 303–22. http://dx.doi.org/10.1016/j.nuclphysb.2004.04.005.

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Riva, Valentina. « Boundary bootstrap principle in two-dimensional integrable quantum field theories ». Nuclear Physics B 604, n^o 3 (juin 2001) : 511–36. http://dx.doi.org/10.1016/s0550-3213(01)00167-5.

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Mussardo, G., V. Riva, G. Sotkov et G. Delfino. « Kink scaling functions in 2D non-integrable quantum field theories ». Nuclear Physics B 736, n^o 3 (février 2006) : 259–87. http://dx.doi.org/10.1016/j.nuclphysb.2005.12.008.

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LeClair, A., G. Mussardo, H. Saleur et S. Skorik. « Boundary energy and boundary states in integrable quantum field theories ». Nuclear Physics B 453, n^o 3 (octobre 1995) : 581–618. http://dx.doi.org/10.1016/0550-3213(95)00435-u.

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Fring, A., C. Korff et B. J. Schulz. « The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory ». Nuclear Physics B 549, n^o 3 (juin 1999) : 579–612. http://dx.doi.org/10.1016/s0550-3213(99)00216-3.

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31

BABUJIAN, H., et M. KAROWSKI. « TOWARDS THE CONSTRUCTION OF WIGHTMAN FUNCTIONS OF INTEGRABLE QUANTUM FIELD THEORIES ». International Journal of Modern Physics A 19, supp02 (mai 2004) : 34–49. http://dx.doi.org/10.1142/s0217751x04020294.

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The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, the program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.

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Fring, Andreas. « PT -symmetric deformations of integrable models ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 371, n^o 1989 (28 avril 2013) : 20120046. http://dx.doi.org/10.1098/rsta.2012.0046.

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We review recent results on new physical models constructed as -symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero–Moser–Sutherland type and nonlinear integrable field equations of Korteweg–de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero–Moser–Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg–de Vries type are studied with regard to different kinds of -symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.

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BASEILHAC, P., P. GRANGÉ et V. A. FATEEV. « EXACT DUALITY BETWEEN INTEGRABLE DEFORMATIONS OF BCn AND $C_n^{(1)}$ AFFINE TODA THEORIES ». Modern Physics Letters A 13, n^o 12 (20 avril 1998) : 937–51. http://dx.doi.org/10.1142/s0217732398001017.

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Integrable deformations of two affine Toda field theories based on BCn and [Formula: see text] non-simply laced algebras are studied. The proof of quantum integrability of the two theories is given and it is shown that the two theories are dual, corresponding respectively to the weak and strong coupling regimes of an intermediate theory. Perturbative calculations and the bootstrap principle permit the construction of the intermediate quantum field theory which flows from the first to the second with the coupling constant.

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CARACCIOLO, R., F. GLIOZZI et R. TATEO. « A TOPOLOGICAL INVARIANT OF RG FLOWS IN 2D INTEGRABLE QUANTUM FIELD THEORIES ». International Journal of Modern Physics B 13, n^o 24n25 (10 octobre 1999) : 2927–32. http://dx.doi.org/10.1142/s0217979299002757.

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We construct a topological invariant of the renormalization group trajectories of a large class of 2D quantum integrable models, described by the thermodynamic Bethe ansatz approach. A geometrical description of this invariant in terms of triangulations of three-dimensional manifolds is proposed and associated dilogarithm identities are proven.

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Destri, C., et H. J. de Vega. « Integrable quantum field theories and conformal field theories from lattice models in the light-cone approach ». Physics Letters B 201, n^o 2 (février 1988) : 261–68. http://dx.doi.org/10.1016/0370-2693(88)90225-0.

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BASEILHAC, P., et V. A. FATEEV. « FERMION–BOSON DUALITY IN INTEGRABLE QUANTUM FIELD THEORY ». Modern Physics Letters A 13, n^o 35 (20 novembre 1998) : 2807–18. http://dx.doi.org/10.1142/s0217732398002989.

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We introduce and study one-parameter family of integrable quantum field theories. This family has a Lagrangian description in terms of massive Thirring fermions ψ, ψ† and charged bosons χ, [Formula: see text] of complex sinh–Gordon model coupled with BCn affine Toda theory. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are applied to show that under duality transformation, which relates weak and strong coupling regimes of the theory, the fermions ψ, ψ† transform to bosons and χ, [Formula: see text] and vice versa. The scattering amplitudes of neutral particles in this theory coincide exactly with S-matrix of particles in pure BCn Toda theory, i.e. the contribution of charged bosons and fermions to these amplitudes exactly cancel each other. We describe and discuss the symmetry responsible for this compensation property.

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Babujian, H. M., M. Karowski et A. M. Tsvelik. « Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories ». Nuclear Physics B 917 (avril 2017) : 122–53. http://dx.doi.org/10.1016/j.nuclphysb.2017.02.002.

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Alazzawi, Sabina, et Gandalf Lechner. « Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories ». Communications in Mathematical Physics 354, n^o 3 (21 juin 2017) : 913–56. http://dx.doi.org/10.1007/s00220-017-2891-0.

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39

Reshetikhin, N., et F. Smirnov. « Hidden quantum group symmetry and integrable perturbations of conformal field theories ». Communications in Mathematical Physics 131, n^o 1 (juillet 1990) : 157–77. http://dx.doi.org/10.1007/bf02097683.

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40

Bostelmann, Henning, et Daniela Cadamuro. « Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories ». Annales Henri Poincaré 20, n^o 12 (20 septembre 2019) : 3889–926. http://dx.doi.org/10.1007/s00023-019-00847-7.

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Abstract We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh–Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.

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MUSSARDO, G., et P. SIMONETTI. « STRESS-ENERGY TENSOR AND ULTRAVIOLET BEHAVIOR IN MASSIVE INTEGRABLE QUANTUM FIELD THEORIES ». International Journal of Modern Physics A 09, n^o 19 (30 juillet 1994) : 3307–37. http://dx.doi.org/10.1142/s0217751x94001308.

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The short distance behavior of massive integrable quantum field theories is analyzed in terms of the form factor approach. We show that the on-shell dynamics is compatible with different definitions of the stress-energy tensor Tµν(x) of the theory. In terms of form factors, this is equivalent to having a possible nonzero matrix element F1 of the trace of Tµν on a one-particle state. Each choice of F1 induces a different scaling behavior of the massive theory in the ultraviolet limit.

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Castro-Alvaredo, Olalla A., et Emanuele Levi. « Higher particle form factors of branch point twist fields in integrable quantum field theories ». Journal of Physics A : Mathematical and Theoretical 44, n^o 25 (16 mai 2011) : 255401. http://dx.doi.org/10.1088/1751-8113/44/25/255401.

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43

Fabiano, Nicola. « Path integral in quantum field theories ». Vojnotehnicki glasnik 70, n^o 4 (2022) : 993–1016. http://dx.doi.org/10.5937/vojtehg70-35882.

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Introduction/purpose: Starting from the Hamiltonian an alternative description of quantum mechanics has been given, based on the sum of all possible paths between an initial and a final point. Methods: Theoretical methods of mathematical physics. Integral method based on the path integral. Results: The method and concepts of the path integral could be applied to other branches of physics, not limited to quantum mechanics. Conclusions: The Path Integral approach gives a global description of fields, unlike the usual Lagrangian approach which is a local description of fields.

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Saleur, Hubert, et Birgit Wehefritz-Kaufmann. « Integrable quantum field theories with supergroup symmetries : the OSP(1/2) case ». Nuclear Physics B 663, n^o 3 (juillet 2003) : 443–66. http://dx.doi.org/10.1016/s0550-3213(03)00385-7.

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Babujian, H., A. Fring, M. Karowski et A. Zapletal. « Exact form factors in integrable quantum field theories : the sine-Gordon model ». Nuclear Physics B 538, n^o 3 (janvier 1999) : 535–86. http://dx.doi.org/10.1016/s0550-3213(98)00737-8.

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Babujian, Hratchya, Angela Foerster et Michael Karowski. « Exact form factors in integrable quantum field theories : the scaling -Ising model ». Nuclear Physics B 736, n^o 3 (février 2006) : 169–98. http://dx.doi.org/10.1016/j.nuclphysb.2005.12.001.

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FATEEV, V. A., et A. B. ZAMOLODCHIKOV. « CONFORMAL FIELD THEORY AND PURELY ELASTIC S-MATRICES ». International Journal of Modern Physics A 05, n^o 06 (20 mars 1990) : 1025–48. http://dx.doi.org/10.1142/s0217751x90000477.

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Particular perturbations of a 2D Conformal Field Theory leading to Integrable massive Quantum Field Theories are examined. The mass spectra and S-matrices for some models, including the field theory of the Ising Model with magnetic field and “thermal” deformations of the tricritical Ising and 3-state Potts models, are proposed. The hidden Lie-algebraic structures of these spectra and their relation to the Toda systems are discussed.

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Buryak, Alexandr, Boris Dubrovin, Jérémy Guéré et Paolo Rossi. « Integrable Systems of Double Ramification Type ». International Mathematics Research Notices 2020, n^o 24 (18 février 2019) : 10381–446. http://dx.doi.org/10.1093/imrn/rnz029.

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Abstract In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable hierarchies and prove that the quantum DR hierarchy enjoys this property. We determine explicitly the genus $1$ quantum correction and, as an application, compute completely the quantization of the $3$- and $4$-KdV hierarchies (the DR hierarchies for Witten’s $3$- and $4$-spin theories). We then focus on the recursion relation satisfied by the DR Hamiltonian densities and, abstracting from its geometric origin, we use it to characterize and construct a new family of quantum and classical integrable systems that we call of DR type, as they satisfy all of the main properties of the DR hierarchy. In the 2nd part, we obtain new insight towards the Miura equivalence conjecture between the DR and Dubrovin-Zhang (DZ) hierarchies, via a geometric interpretation of the correlators forming the DR tau-function. We then show that the candidate Miura transformation between the DR and DZ hierarchies (which we uniquely identified in our previous paper) indeed turns the DZ Poisson structure into the standard form. Eventually, we focus on integrable hierarchies associated with rank-$1$ cohomological field theories and their deformations, and we prove the DR/DZ equivalence conjecture up to genus $5$ in this context.

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Dorey, Patrick, Simone Faldella, Stefano Negro et Roberto Tateo. « The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 371, n^o 1989 (28 avril 2013) : 20120052. http://dx.doi.org/10.1098/rsta.2012.0052.

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The theory of classically integrable nonlinear wave equations and the Bethe ansatz systems describing massive quantum field theories defined on an infinite cylinder are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper, we shall extend this link to the case of the classical and quantum versions of the Tzitzéica–Bullough–Dodd model.

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EVANS, JONATHAN M., et JENS OLE MADSEN. « QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α) ». International Journal of Modern Physics A 14, n^o 16 (30 juin 1999) : 2551–80. http://dx.doi.org/10.1142/s0217751x99001275.

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We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

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Articles de revues sur le sujet « Integrable quantum field theories »

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