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 Using Covariant Polarisation Sums in QCD

2022 ◽  
Vol 137 (1) ◽  
Author(s):  
M. Kachelrieß ◽  
M. N. Malmquist
Keyword(s):  
Gauge Boson ◽  
Ward Identity ◽  
Gauge Theories ◽  
Feynman Rule ◽  
Optical Theorem ◽  
Gauge Bosons ◽  
Abelian Gauge ◽  
Feynman Gauge ◽  
Cross Terms ◽  
External Gauge

AbstractCovariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

scholarly journals TENSIONLESS BRANES AND THE NULL STRING CRITICAL DIMENSION

1998 ◽  
Vol 13 (32) ◽  
pp. 2571-2583 ◽  
Author(s):  
P. BOZHILOV
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Critical Dimension ◽  
Space Time ◽  
Operator Ordering ◽  
Vacuum States ◽  
Constraint Algebra ◽  
The One ◽  
Null String

BRST quantization is carried out for a model of p-branes with second-class constraints. After extension of the phase space, the constraint algebra coincides with the one of null string when p =1. It is shown that in this case one can or cannot obtain critical dimension for the null string, depending on the choice of the operator ordering and the corresponding vacuum states. When p>1, operator orderings leading to critical dimension in the p=1 case are not allowed. Admissible orderings give no restrictions on the dimension of the embedding space–time. Finally, a generalization to supersymmetric null branes is proposed.

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 GAUGE CONSISTENT WILSON RENORMALIZATION GROUP II: THE NON-ABELIAN CASE

2000 ◽  
Vol 15 (14) ◽  
pp. 2153-2179 ◽  
Author(s):  
M. SIMIONATO
Keyword(s):  
Renormalization Group ◽  
Gauge Theories ◽  
Beta Function ◽  
Ward Identities ◽  
Abelian Gauge ◽  
Axial Gauge ◽  
Abelian Case ◽  
Group Ii ◽  
The One ◽  
Wilson Renormalization Group

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed.

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 Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

Fixed point structure of 3D abelian gauge theories

1999 ◽  
Author(s):  
Taichi Itoh ◽  
Yoonbai Kim
Keyword(s):  
Fixed Point ◽  
Gauge Theories ◽  
Abelian Gauge
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