Lorentz Covariance and the Canonical Quantization of Non-Abelian Gauge Theories

1971 ◽  
Vol 3 (2) ◽  
pp. 400-408 ◽  
Author(s):  
Michael J. Russo
Keyword(s):  
Gauge Theories ◽  
Canonical Quantization ◽  
Abelian Gauge ◽  
Lorentz Covariance

JET-GAUGE GROUPS AS BASIC SYMMETRIES OF NON-LINEAR SIGMA AND YANG–MILLS MODELS AND QUANTIZATION

2012 ◽  
Vol 09 (02) ◽  
pp. 1260006
Author(s):  
VICTOR ALDAYA ◽  
MANUEL CALIXTO ◽  
JULIO GUERRERO ◽  
FRANCISCO F. LOPEZ-RUIZ
Keyword(s):  
Sigma Models ◽  
Gauge Theories ◽  
Canonical Quantization ◽  
Group Approach ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Yang Mills ◽  
Non Linear ◽  
Non Linear Systems ◽  
Linear Sigma Models

The quantum description of non-linear systems finds a deep obstruction in the Canonical Quantization framework and Non-Linear Sigma Models constitute the best representatives. In this paper, we face the quantization of such systems on the grounds of a Group Approach to Quantization, and extend the algorithm to the specific case of massive Non-Abelian gauge theories. The basic geometric structures behind are the so-called "jet-gauge groups".

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.

Entanglement entropy in Abelian gauge theories

2009 ◽  
Vol 72 (9) ◽  
pp. 1601-1605
Author(s):  
P. V. Buividovich ◽  
M. I. Polikarpov
Keyword(s):  
Gauge Theories ◽  
Entanglement Entropy ◽  
Abelian Gauge
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