Phase Space Expansions in Quantum Field Theory

1987 ◽  
pp. 160-183
Author(s):  
J. Feldman
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Quantum Field

scholarly journals PHASE SPACE PROPERTIES OF CHARGED FIELDS IN THEORIES OF LOCAL OBSERVABLES

1995 ◽  
Vol 07 (04) ◽  
pp. 527-557 ◽  
Author(s):  
D. BUCHHOLZ ◽  
C. D’ANTONI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Space Analysis ◽  
Algebraic Quantum ◽  
Thermal Features ◽  
Local Observables

Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic quantum field theory are reviewed and the underlying ideas are outlined.

Quantum field theory in phase space

2019 ◽  
Vol 34 (08) ◽  
pp. 1950037 ◽  
Author(s):  
R. G. G. Amorim ◽  
F. C. Khanna ◽  
A. P. C. Malbouisson ◽  
J. M. C. Malbouisson ◽  
A. E. Santana
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Phase Space ◽  
Relativistic Quantum ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Quantization Rules

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the Hilbert space has the phase space content, a symplectic Hilbert space. The state is described by a quasi-amplitude of probability, which is a sort of wave function in phase space, associated with the Wigner function. The quantum field theory in phase space is then constructed, including the quantization rules for the Klein–Gordon and the Dirac fields, the derivation of the electrodynamics in phase space and elements of a relativistic quantum kinetic theory. Towards a physical interpretation of the theory, propagators are associated with the corresponding Wigner functions. The Feynman rules follow accordingly with vertices similar to those of usual non-Abelian quantum field theories.

SECTOR DECOMPOSITION

2008 ◽  
Vol 23 (10) ◽  
pp. 1457-1486 ◽  
Author(s):  
GUDRUN HEINRICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
General Algorithm ◽  
Constructive Method ◽  
Quantum Field ◽  
Matrix Elements ◽  
Feynman Parameter ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multiloop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

scholarly journals Worldline colour fields and non-Abelian quantum field theory

2018 ◽  
Vol 182 ◽  
pp. 02038 ◽  
Author(s):  
James P. Edwards ◽  
Olindo Corradini
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Wilson Loop ◽  
Degrees Of Freedom ◽  
Gauge Potential ◽  
Quantum Field ◽  
Abelian Field ◽  
Constraint Algebra ◽  
Chern Simons

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline “colour” fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on S1 for simple representations of SU(N).

CANONICAL PHASE, TOPOLOGICAL INVARIANT AND REPRESENTATION THEORY

1990 ◽  
Vol 05 (12) ◽  
pp. 917-925 ◽  
Author(s):  
HIROSHI KURATSUJI ◽  
KEN-ICHI TAKADA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Phase Space ◽  
General Scheme ◽  
Geometric Quantization ◽  
Topological Invariant ◽  
Quantum Field ◽  
Compact Lie Groups ◽  
Generalized Phase Space

We show that the non-integrable phase defined over the generalized phase space, which is called the canonical phase, yields the topological quantization that reveals the connection with the irreducible representation of a certain class of compact Lie groups. Although this consequence by itself is already known in mathematics under the general scheme named geometric quantization, it has not yet been fully appreciated in physics except for some specific problems. The descriptive technique adopted here seems fresh enough to commit itself to the topological aspect of quantum mechanics even including quantum field theory.

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