Dynamical breaking of gauge symmetry in Abelian gauge theories in two dimensions

1983 ◽  
Vol 27 (2) ◽  
pp. 395-405
Author(s):  
Hisakazu Minakata
Keyword(s):  
Gauge Symmetry ◽  
Gauge Theories ◽  
Two Dimensions ◽  
Abelian Gauge ◽  
Dynamical Breaking

SPECTRAL FLOW OF HERMITIAN WILSON–DIRAC OPERATOR AND THE INDEX THEOREM IN ABELIAN GAUGE THEORIES ON FINITE LATTICES

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1943-1950 ◽  
Author(s):  
T. FUJIWARA
Keyword(s):  
Dirac Operator ◽  
Gauge Theories ◽  
Index Theorem ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Continuous Family ◽  
Spectral Flow ◽  
Abelian Gauge ◽  
Characteristic Structure ◽  
Finite Lattices

The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field configurations. It is also argued that in two dimensions the eigenvalue spectra for some special but nontrivial background gauge fields can be described by a set of universal polynomials and the index can be found exactly.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

scholarly journals Covariant phase space and soft factorization in non-Abelian gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Temple He ◽  
Prahar Mitra
Keyword(s):  
Phase Space ◽  
Ward Identity ◽  
Gauge Theories ◽  
Minkowski Spacetime ◽  
Soft Gluon ◽  
Careful Study ◽  
Abelian Gauge ◽  
Gauge Sector ◽  
Vacuum States ◽  
The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

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