scholarly journals Renormalization of gauge theories in the background-field approach

2018 ◽  
Vol 2018 (7) ◽  
Author(s):  
Andrei O. Barvinsky ◽  
Diego Blas ◽  
Mario Herrero-Valea ◽  
Sergey M. Sibiryakov ◽  
Christian F. Steinwachs
Keyword(s):  
Gauge Theories ◽  
Background Field ◽  
Field Approach

scholarly journals GENERAL FORMULA FOR THE FOUR-QUARK CONDENSATE AND VACUUM FACTORIZATION ASSUMPTION

2008 ◽  
Vol 23 (10) ◽  
pp. 1507-1520 ◽  
Author(s):  
HONG-SHI ZONG ◽  
DENG-KE HE ◽  
FENG-YAO HOU ◽  
WEI-MIN SUN
Keyword(s):  
General Formula ◽  
Linear Response ◽  
Chemical Potential ◽  
Background Field ◽  
Quark Propagator ◽  
Quark Condensate ◽  
Sum Rule ◽  
Factorization Problem ◽  
Field Approach ◽  
General Method

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate [Formula: see text]. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for [Formula: see text] holds only when the dressed vertex is taken to be the bare one. This property also holds for all other types of four-quark condensate. By comparing this formula with the general expression for the corresponding vacuum susceptibility, it is found that there exists some intrinsic relation between these two quantities, which are usually treated as independent phenomenological inputs in the QCD sum rule external field approach. The above results are also generalized to the case of finite chemical potential and the factorization problem of the four-quark condensate at finite chemical potential is discussed.

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 The mixed 0-form/1-form anomaly in Hilbert space: pouring the new wine into old bottles

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Andrew A. Cox ◽  
Erich Poppitz ◽  
F. David Wandler
Keyword(s):  
Hilbert Space ◽  
Gauge Group ◽  
Operator Algebra ◽  
Central Extension ◽  
Gauge Theories ◽  
Finite Size ◽  
Background Field ◽  
Symmetry Operator ◽  
Global Symmetry ◽  
Global Center

Abstract We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry. We canonically quantize on 𝕋3, in a fixed background field gauging the 1-form symmetry. We show that the mixed 0-form/1-form ’t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite- size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in SU(N) theories, with or without adjoint fermions, as well as with their conjectured infrared phases.

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