scholarly journals Phase space properties and the short distance structure in quantum field theory

2005 ◽  
Vol 46 (5) ◽  
pp. 052301 ◽  
Author(s):  
Henning Bostelmann
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Short Distance ◽  
Quantum Field

scholarly journals SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

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.

FINITE CASIMIR EFFECT IN QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (10) ◽  
pp. 1677-1702 ◽  
Author(s):  
A. BLASI ◽  
R. COLLINA ◽  
J. SASSARINI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Casimir Effect ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Complete Control ◽  
Soft Term ◽  
Distance Behavior

The computation of the Casimir effect is directly linked to the modification of the vacuum energy due to the presence of boundaries. In order to have complete control of the short distance behavior also near the boundary, the analysis is performed in the precise framework of a local, renormalizable quantum field theory which includes the boundary contributions. We show that the presence of soft terms at the boundary, needed to implement Robin's conditions, introduces a free parameter in the final, finite answer, a parameter which has no natural normalization condition within the scheme. We discuss in detail a free massless scalar field in R3 with plane and cylindric boundaries; in particular the second case, where the boundary soft term is essential to remove sub-leading short distance divergencies, suffers the mentioned indeterminacy, which might be removed by a phenomenological interpretation relating the soft term to a microscopic description of the boundary.

scholarly journals Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.

1998 ◽  
Vol 10 (06) ◽  
pp. 775-800 ◽  
Author(s):  
D. Buchholz ◽  
R. Verch
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Relativistic Quantum ◽  
Free Field ◽  
Scaling Limit ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Spatial Dimensions ◽  
Local Observables

The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article this method is applied to the simple example of massive free field theory in s=1,2 and 3 spatial dimensions. Not quite unexpectedly, one obtains for s=2,3 in the scaling (short distance) limit the algebra of local observables in massless free field theory. The case s=1 offers, however, some surprises. There the algebra of observables acquires in the scaling limit a non-trivial center and describes charged physical states satisfying Gauss' law. The latter result is of relevance for the interpretation of the Schwinger model at short distances and illustrates the conceptual and computational virtues of the method.

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