The one-loop Green’s functions of dimensionally reduced gauge theories

Pramana ◽  
1988 ◽  
Vol 30 (3) ◽  
pp. 173-182 ◽  
Author(s):  
S V Ketov ◽  
Y S Prager
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
The One

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

scholarly journals Composite and Background Fields in Non-Abelian Gauge Models

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1985
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Effective Action ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Systematic Analysis ◽  
Generating Functional ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Background Fields

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory.

Sp(2) COVARIANT QUANTIZATION OF GAUGE THEORIES

1991 ◽  
Vol 06 (22) ◽  
pp. 2051-2057 ◽  
Author(s):  
P. M. LAVROV
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Brst Quantization ◽  
Covariant Quantization ◽  
Gauge Dependence

The gauge dependence of the Green's functions generating functionals in the framework of extended Lagrangian BRST quantization is investigated.

scholarly journals ON THE STRUCTURE OF QUANTUM GAUGE THEORIES WITH EXTERNAL FIELDS

1998 ◽  
Vol 13 (23) ◽  
pp. 4077-4089 ◽  
Author(s):  
S. FALKENBERG ◽  
B. GEYER ◽  
P. LAVROV ◽  
P. MOSHIN
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
External Fields ◽  
Ward Identities ◽  
Gauge Dependence ◽  
General Gauge

We consider generating functionals of Green's functions with external fields in the framework of BV and BLT quantization schemes for general gauge theories. The corresponding Ward identities are obtained, and the gauge dependence is studied.

scholarly journals RELATING CALCULATIONS AND RENORMALIZATION IN AXIAL AND LORENTZ GAUGES AND GAUGE-INDEPENDENCE

2005 ◽  
Vol 20 (28) ◽  
pp. 6437-6449
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Wave Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Wave Function Renormalization ◽  
Renormalization Procedure ◽  
Point Function ◽  
Starting Point ◽  
Loop Approximation ◽  
The Difference ◽  
The One

We study further the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the one-loop approximation for the wave function renormalization and the identity of the β-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the one-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the β-functions in the two gauges.

Erratum: Green's functions of composite operators and bound states in gauge theories

1990 ◽  
Vol 41 (10) ◽  
pp. 3279-3279 ◽  
Author(s):  
V. P. Gusynin ◽  
V. A. Kushnir ◽  
V. A. Miransky
Keyword(s):  
Bound States ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions

Green’s functions of composite operators and bound states in gauge theories

1989 ◽  
Vol 39 (8) ◽  
pp. 2355-2367 ◽  
Author(s):  
V. P. Gusynin ◽  
V. A. Kushnir ◽  
V. A. Miransky
Keyword(s):  
Bound States ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions
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