Method for approximate evaluation of path integrals using perturbation theory with convergent series. II. Euclidean quantum field theory

1996 ◽  
Vol 109 (1) ◽  
pp. 1294-1301 ◽  
Author(s):  
V. V. Belokurov ◽  
Yu. P. Solov'ev ◽  
E. T. Shavgulidze
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Path Integrals ◽  
Convergent Series ◽  
Quantum Field ◽  
Approximate Evaluation ◽  
Euclidean Quantum Field Theory

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals CAUSAL PERTURBATION THEORY IN TERMS OF RETARDED PRODUCTS, AND A PROOF OF THE ACTION WARD IDENTITY

2004 ◽  
Vol 16 (10) ◽  
pp. 1291-1348 ◽  
Author(s):  
MICHAEL DÜTSCH ◽  
KLAUS FREDENHAGEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Ward Identity ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Local Construction ◽  
Free Parameters ◽  
Classical Fields

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann [42]. In our formalism the entries of the retarded products are local functionals of the off-shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's "Action Ward Identity" [45]. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald [32]. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

scholarly journals INTERACTION MEASURES ON THE SPACE OF DISTRIBUTIONS OVER THE FIELD OF p-ADIC NUMBERS

2003 ◽  
Vol 06 (03) ◽  
pp. 389-411 ◽  
Author(s):  
ANATOLY N. KOCHUBEI ◽  
MUSTAFA R. SAIT-AMETOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operator ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Quantum Field ◽  
Pseudo Differential Operator ◽  
Schwartz Distributions ◽  
Space Of Distributions ◽  
Euclidean Quantum Field Theory

We construct measures on the space [Formula: see text], n≤4, of Bruhat–Schwartz distributions over the field of p-adic numbers, corresponding to finite volume polynomial interactions in a p-adic analog of the Euclidean quantum field theory. In contrast to earlier results in this direction, our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudo-differential operator over [Formula: see text]. Analogs of the Euclidean P(φ)-theories with free and half-Dirichlet boundary conditions are considered.

scholarly journals Hadron physics from lattice QCD

2016 ◽  
Vol 25 (07) ◽  
pp. 1642008 ◽  
Author(s):  
Wolfgang Bietenholz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Quantum Field ◽  
Chiral Perturbation ◽  
Hadron Physics ◽  
Lattice Regularization ◽  
Sign Problem ◽  
Hadron Masses ◽  
Basic Ideas

We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last, we address two outstanding issues: topological freezing and the sign problem.

Some quantum field theory aspects of the superspace quantization of general relativity

1976 ◽  
Vol 351 (1665) ◽  
pp. 209-232 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Perturbation Theory ◽  
Constraint Equation ◽  
Mathematical Structure ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Status

An investigation is started into a possible mathematical structure of the Wheeler-DeWitt superspace quantization of general relativity. The emphasis is placed throughout on quantum field theory aspects of the problem and topics discussed include canonical commutation relations in a triad basis, the status of the constraint equation and the rôle played by perturbation theory.

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