scholarly journals ELECTRIC-MAGNETIC DUALITY AND THE “LOOP REPRESENTATION” IN ABELIAN GAUGE THEORIES

1996 ◽  
Vol 11 (13) ◽  
pp. 1107-1114 ◽  
Author(s):  
LORENZO LEAL
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Topological Algebra ◽  
Geometric Representation ◽  
Abelian Gauge ◽  
Dual Algebra ◽  
Nonlocal Operators ◽  
Canonical Algebra

Abelian gauge theories are quantized in a geometric representation that generalizes the loop representation and treats electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of nonlocal operators that resembles the order-disorder dual algebra of ’t Hooft. These dual operators provide a complete description of the physical phase space of the theories.

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.

scholarly journals SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES

1995 ◽  
Vol 10 (10) ◽  
pp. 1449-1463 ◽  
Author(s):  
G. DI CECIO ◽  
G. PAFFUTI
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Perturbative Expansion ◽  
Abelian Gauge ◽  
Nonlocal Operators ◽  
Abelian Gauge Theory ◽  
Effective Lagrangian ◽  
Local Operators

We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.

scholarly journals ON THE EQUIVALENCE BETWEEN TOPOLOGICALLY AND NON-TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORIES

2000 ◽  
Vol 15 (02) ◽  
pp. 121-131 ◽  
Author(s):  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Correlation Function ◽  
Gauge Theory ◽  
Phase Space ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
First Order ◽  
Space Extension ◽  
Canonical Variables ◽  
Canonical Approach ◽  
Total Divergence

We analyze the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are Stückelberg formulation of (a) a first-order formulation involving one- and two-form fields, (b) Proca theory, and (c) massive Kalb–Ramond theory. We first quantize these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.

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 CONSTRAINED DYNAMICS OF THE COUPLED ABELIAN TWO-FORM

1993 ◽  
Vol 08 (25) ◽  
pp. 2403-2412 ◽  
Author(s):  
AMITABHA LAHIRI
Keyword(s):  
Phase Space ◽  
Gauge Field ◽  
Antisymmetric Tensor ◽  
Abelian Gauge ◽  
Constrained Dynamics ◽  
Duality Transformations ◽  
Tensor Potential

I present the reduction of phase space of the theory of an antisymmetric tensor potential coupled to an Abelian gauge field, using Dirac's procedure. Duality transformations on the reduced phase space are also discussed.

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