scholarly journals INFINITE QUANTUM GROUP SYMMETRY OF FIELDS IN MASSIVE 2D QUANTUM FIELD THEORY

1992 ◽  
Vol 07 (13) ◽  
pp. 2997-3022 ◽  
Author(s):  
ANDRÉ LECLAIR ◽  
F. A. SMIRNOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Group ◽  
Form Factors ◽  
Adjoint Action ◽  
Momentum Tensor ◽  
Group Symmetry ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
Symmetry Generators

Starting from a given S-matrix of an integrable quantum field theory in 1 + 1 dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the form factors of descendents. The braiding relations of quantum field multiplets is shown to be given by the universal ℛ-matrix. We develop in some detail the case of infinite-dimensional Yangian symmetry. We show that the quantum double of the Yangian is a Hopf algebra deformation of a level zero Kac–Moody algebra that preserves its finite-dimensional Lie subalgebra. The fields form infinite-dimensional Verma module representations; in particular, the energy–momentum tensor and isotopic current are in the same multiplet.

scholarly journals Infinite dimensional Langevin equation and Fokker-Planck equation

1981 ◽  
Vol 81 ◽  
pp. 177-223 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Partial Differential Equations ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theory Theory ◽  
Quantum Field ◽  
Filtering Theory ◽  
Infinite Dimensional

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

scholarly journals SCHIZOSYMMETRY: A NEW PARADIGM FOR SUPERFIELD EXPANSIONS

1994 ◽  
Vol 09 (25) ◽  
pp. 2305-2313 ◽  
Author(s):  
R. DELBOURGO ◽  
P.D. JARVIS ◽  
ROLAND C. WARNER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Model Building ◽  
Space Time ◽  
Unified Model ◽  
Quantum Field ◽  
New Paradigm ◽  
Field Transformation ◽  
Component Field ◽  
Symmetry Generators

A new principle of ‘schizosymmetry’ is proposed for interpreting superfield expansions over Grassmann parameters in quantum field theory. Symmetry generators T phys , determining component field transformation properties, are allowed to depend on the grading via T phys =Tℙ e +T′ℙ o , where ℙ e and ℙ o are the projections onto even and odd components in the Grassmann coordinates, respectively, and T and T′ correspond to different representations. Examples are given for both internal and space-time schizosymmetry. In the latter case, superfield expansions have components with both integer and half-integer spin. A program for the Lagrangian realization of schizosymmetry, including unified model building, is outlined.

scholarly journals An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
John Mashford
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Bundles ◽  
Principal Bundle ◽  
Adjoint Action ◽  
Flat Space ◽  
Quantum Field ◽  
Euclidean Topology ◽  
Fermion Fields ◽  
Classical Quantum

This paper gives an introduction to certain classical physical theories described in the context of locally Minkowskian causal structures (LMCSs). For simplicity of exposition we consider LMCSs which have locally Euclidean topology (i.e., are manifolds) and hence are Möbius structures. We describe natural principal bundle structures associated with Möbius structures. Fermion fields are associated with sections of vector bundles associated with the principal bundles while interaction fields (bosons) are associated with endomorphisms of the space of fermion fields. Classical quantum field theory (the Dirac equation and Maxwell’s equations) is obtained by considering representations of the structure group K⊂SU(2,2) of a principal bundle associated with a given Möbius structure where K, while being a subset of SU(2,2), is also isomorphic to SL2,C×U(1). The analysis requires the use of an intertwining operator between the action of K on R4 and the adjoint action of K on su⁡(2,2) and it is shown that the Feynman slash operator, in the chiral representation for the Dirac gamma matrices, has this intertwining property.

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