scholarly journals GAUGE INVARIANCE AND THE GOLDSTONE THEOREM

2011 ◽  
Vol 26 (19) ◽  
pp. 1381-1392 ◽  
Author(s):  
GERALD S. GURALNIK
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Elementary Particles ◽  
Max Planck ◽  
Goldstone Theorem ◽  
Zero Mass ◽  
Unified Theories

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

A Problem of Mass

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Long Range ◽  
Gauge Invariance ◽  
Weak Interactions ◽  
Elementary Particles ◽  
Gauge Invariant ◽  
Zero Mass ◽  
Gauge Symmetries ◽  
Symmetry Properties ◽  
Long Range Interactions ◽  
The Masses

This chapter examines the constraints coming from the symmetry properties of the fundamental interactions on the possible values of the masses of elementary particles. We first establish a relation between the range of an interaction and the mass of the particle which mediates it. This relation implies, in particular, that long-range interactions are mediated by massless particles. Then we argue that gauge invariant interactions are long ranged and, therefore, the associated gauge particles must have zero mass. Second, we look at the properties of the constituents of matter, the quarks and the leptons. We introduce the notion of chirality and we show that the known properties of weak interactions, combined with the requirement of gauge invariance, force these particles also to be massless. The conclusion is that gauge symmetries appear to be incompatible with massive elementary particles, in obvious contradiction with experiment. This is the problem of mass.

On the Brout–Englert–Higgs–Guralnik–Hagen–Kibble Mechanism in Quantum Gravity

2018 ◽  
Vol 26 (1) ◽  
pp. 110-116
Author(s):  
Gerard ‘t Hooft
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Elementary Particles ◽  
Local Gauge ◽  
Gravitational Forces ◽  
Local Gauge Invariance

Local gauge invariance can materialise in different ways in theories for quantised elementary particles. It is less well-known, however, that a quite similar situation also occurs in the Einstein–Hilbert formalism for the gravitational forces. This may have important consequences for quantum theory. At first sight one may even think that it renders gravity renormalisable, just as happens in local gauge theories, but in gravity the truth is more puzzling.

Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors

1973 ◽  
Vol 8 (12) ◽  
pp. 4498-4509 ◽  
Author(s):  
Marcus T. Grisaru ◽  
Howard J. Schnitzer ◽  
Hung-Sheng Tsao
Keyword(s):  
Gauge Theories ◽  
Elementary Particles

scholarly journals Gauge Invariance and Mass Gap in (2+1)-Dimensional Yang–Mills Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1161-1171 ◽  
Author(s):  
Dimitra Karabali ◽  
V. P. Nair
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mass Gap ◽  
Spatial Dimensions

In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.

scholarly journals NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
Author(s):  
A. ASTE ◽  
G. SCHARF
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Fundamental Concept ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Vector Bosons ◽  
Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

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