scholarly journals Chiral Symmetry Breaking and Nonperturbative Scale Anomaly in Gauge Field Theories

1989 ◽  
Vol 81 (2) ◽  
pp. 426-450 ◽  
Author(s):  
V. A. Miransky ◽  
V. P. Gusynin
Keyword(s):  
Symmetry Breaking ◽  
Gauge Field ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Gauge Field Theories ◽  
Field Theories

Symmetries, chiral symmetry breaking, and renormalization

2021 ◽  
pp. 292-323
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Symmetry Properties ◽  
Physical Consequences ◽  
Effective Models ◽  
Continuous Symmetries ◽  
Limiting Case

Most quantum field theories (QFT) of physical interest exhibit symmetries, exact symmetries or symmetries with soft (e.g. linear) breaking. This chapter deals only with linear continuous symmetries corresponding to compact Lie groups. When the bare action has symmetry properties, to preserve the symmetry it is first necessary to find a symmetric regularization. The symmetry properties of the QFT then imply relations between connected correlation functions, and vertex functions, called Ward–Takahashi (WT) identities, which describe the physical consequences of the symmetry. WT identities also constrain UV divergences, and the counter-terms that render the theory finite are not of most general form allowed by power counting. As a consequence the renormalized action is expected to keep some trace of the initial symmetry. Such an analysis is based on a perturbative loop expansion. More generally, some non-trivial relations survive when to the action are added terms that induce a soft breaking of symmetry (i.e. by relevant terms). The specific examples of linear symmetry breaking, and the very important limiting case of spontaneous symmetry breaking, and quadratic symmetry breaking are examined. Finally, as an application, the example of chiral symmetry breaking in low-energy effective models of hadron physics is discussed.

Aspects of dynamical symmetry breaking in gauge field theories

1989 ◽  
Vol 323 (3) ◽  
pp. 493-512 ◽  
Author(s):  
William A. Bardeen ◽  
C.N. Leung ◽  
S.T. Love
Keyword(s):  
Symmetry Breaking ◽  
Gauge Field ◽  
Dynamical Symmetry ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Dynamical Symmetry Breaking

scholarly journals HOW TO TREAT γ5

1998 ◽  
Vol 13 (17) ◽  
pp. 2991-3050 ◽  
Author(s):  
HUNG CHENG ◽  
S. P. LI
Keyword(s):  
Symmetry Breaking ◽  
Vector Meson ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Field ◽  
Dimensional Regularization ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Chiral Fermion ◽  
Gauge Invariant ◽  
The Past

In the past two decades, Dyson's formalism of renormalization has been mostly superceded by dimensional regularization, particularly in the treatment of quantum gauge field theories with spontaneous symmetry breaking or those with chiral fermions. In this paper, we shall carry out explicitly Dyson's subtraction program, making it applicable to such field theories. In particular, we show with the example of the Abelian–Higgs theory how to handle amplitudes of chiral fermions. We show that these amplitudes which involve the γ5 matrix can be calculated in an unambiguous and gauge invariant way. This is done by establishing the subtraction conditions for the propagator of a chiral fermion as well as those for the VVV amplitude, when V denotes the vector meson. The renormalized constants are chosen to satisfy the Ward–Takahashi identities. As a demonstration, we calculate the next-lowest order correction of the anomaly in the Abelian–Higgs model and find that it vanishes.

scholarly journals Impact of center vortex removal on chiral symmetry breaking in SU(3) gauge field theory

2011 ◽  
Author(s):  
Derek Leinweber ◽  
S. Mahbub ◽  
Waseem Kamleh ◽  
Peter J Moran ◽  
A. G. Williams
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Gauge Field ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Gauge Field Theory ◽  
Center Vortex
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