Background-field method and the renormalization of non-Abelian gauge theories in curved space-time

1983 ◽  
Vol 27 (8) ◽  
pp. 1803-1813 ◽  
Author(s):  
David J. Toms
Keyword(s):  
Gauge Theories ◽  
Background Field ◽  
Field Method ◽  
Space Time ◽  
Abelian Gauge ◽  
Curved Space ◽  
Background Field Method

Gauge theories at finite temperature and the background field method

1990 ◽  
Vol 242 (3-4) ◽  
pp. 412-414 ◽  
Author(s):  
J. Antikainen ◽  
M. Chaichian ◽  
N.R. Pantoja ◽  
J.J. Salazar
Keyword(s):  
Finite Temperature ◽  
Gauge Theories ◽  
Background Field ◽  
Field Method ◽  
Background Field Method

Quantum gauge theories

2021 ◽  
pp. 223-268
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Background Field ◽  
Field Method ◽  
Extensive Discussion ◽  
Functional Integrals ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Background Field Method ◽  
Popov Method

This chapter, which is the last chapter in Part I, is devoted to an extensive discussion of quantum gauge theories, which is based on functional integrals and Lagrangian quantization. After introducing the notion of a Yang-Mills gauge theory, the Faddeev-Popov method (also known as the DeWitt-Faddeev-Popov procedure) is explained. Starting from this point, the BRST symmetry is formulated, and the corresponding Ward identities (called Slavnov-Taylor identities in some cases) established. More specialized subjects, such as the gauge dependence of effective action and the background field method, are dealt with in detail. In addition, Yang-Mills theory is analyzed as a primary example of general theorems concerning the renormalization of gauge theories.

scholarly journals INDUCED COLOR CURRENT BY GLUON IN BACKGROUND QCD

2001 ◽  
Vol 10 (06) ◽  
pp. 483-499 ◽  
Author(s):  
Q. WANG ◽  
C.-W. KAO ◽  
G. C. NAYAK ◽  
W. GREINER
Keyword(s):  
Background Field ◽  
Field Method ◽  
Integral Approach ◽  
Asymptotic Freedom ◽  
Displacement Current ◽  
Inhomogeneous Field ◽  
Induced Current ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Background Field Method

By using the background field method of QCD in a path integral approach, we derive the equation of motion for the classical chromofield and that for the gluon in a system containing the gluon and the classical chromofield simultaneously. This inhomogeneous field equation contains an induced current term, which is the expectation value of a combination of composite operators including linear, square and cubic terms of the gluon field. We also derive identities for the current from gauge invariance and calculate the current at the leading order where the current induced by the gluon is opposite in sign to that induced by the quark. This is just the feature of the non-Abelian gauge field theory which has asymptotic freedom. Physically, the induced current can be treated as a "displacement" current in the polarized vacuum, and its effect is equivalent to redefining the field and the coupling constant.

scholarly journals Two-loop renormalisation of gauge theories in 4D implicit regularisation and connections to dimensional methods

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
A. Cherchiglia ◽  
D. C. Arias-Perdomo ◽  
A. R. Vieira ◽  
M. Sampaio ◽  
B. Hiller
Keyword(s):  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Background Field ◽  
Field Method ◽  
Loop Order ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Lorentz Algebra ◽  
Background Field Method

AbstractWe compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

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