scholarly journals Gauge Boson Condensation and Symmetry Breaking Patterns in Non-Abelian Gauge Theories

1982 ◽  
Vol 67 (1) ◽  
pp. 297-308 ◽  
Author(s):  
T. Inami ◽  
S. Watamura
Keyword(s):  
Symmetry Breaking ◽  
Gauge Boson ◽  
Gauge Theories ◽  
Abelian Gauge

Symmetry Breaking in Non-Abelian Gauge Theories

1967 ◽  
Vol 155 (5) ◽  
pp. 1554-1561 ◽  
Author(s):  
T. W. B. Kibble
Keyword(s):  
Symmetry Breaking ◽  
Gauge Theories ◽  
Abelian Gauge

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 Strong dynamics, composite Higgs and the conformal window

2016 ◽  
Vol 31 (22) ◽  
pp. 1643003 ◽  
Author(s):  
Daniel Nogradi ◽  
Agostino Patella
Keyword(s):  
Mass Spectrum ◽  
Symmetry Breaking ◽  
Recent Progress ◽  
Gauge Theories ◽  
Model Building ◽  
Dynamical Symmetry ◽  
Higgs Particle ◽  
Abelian Gauge ◽  
Composite Higgs

We review recent progress in the lattice investigations of near-conformal non-Abelian gauge theories relevant for dynamical symmetry breaking and model building of composite Higgs models. The emphasis is placed on the mass spectrum and the running renormalized coupling. The role of a light composite scalar isosinglet particle as a composite Higgs particle is highlighted.

scholarly journals RENORMALIZATION GROUP AND DYNAMICS OF SUPERSYMMETRIC GAUGE THEORIES

2001 ◽  
Vol 16 (11) ◽  
pp. 1861-1873 ◽  
Author(s):  
K. KONISHI
Keyword(s):  
Renormalization Group ◽  
Symmetry Breaking ◽  
Gauge Theories ◽  
Dynamical Symmetry ◽  
Supersymmetric Gauge Theories ◽  
Abelian Gauge ◽  
Dynamical Symmetry Breaking ◽  
Supersymmetric Gauge

We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative β functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of SU(nc), USp(2nc) and SO(nc) theories are discussed.

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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