scholarly journals ON THE SYMMETRY OF THE VACUUM IN THEORIES WITH "SPONTANEOUS SYMMETRY BREAKING"

2011 ◽  
Vol 26 (09) ◽  
pp. 1493-1544 ◽  
Author(s):  
ALEJANDRO PEREZ ◽  
DANIEL SUDARSKY
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Topological Defects ◽  
Quantum Field ◽  
Mass Generation ◽  
Symmetric Scheme ◽  
Gauge Symmetries ◽  
Symmetric Vacuum ◽  
The Common

We review the usual account of the phenomena of spontaneous symmetry breaking, pointing out the common misunderstandings surrounding the issue, in particular within the context of quantum field theory. In fact, the common explanations one finds in this context, indicate that under certain conditions corresponding to the situation called spontaneous symmetry breaking, the vacuum of the theory does not share the symmetries of the Lagrangian. We explain in detail why this statement is incorrect in general, and in what limited set of circumstances such a situation could arise. We concentrate on the case of global symmetries, for which we found no satisfactory exposition in the existing literature, and briefly comment on the case of gauge symmetries where, although insufficiently publicized, accurate and complete descriptions exist. We briefly discuss the implications for the phenomenological manifestations usually attributed to the phenomena of spontaneous symmetry breaking, analyzing which might be affected by our analysis and which are not. In particular we describe the mass generation mechanism in a fully symmetric scheme (i.e. with a totally symmetric vacuum), and briefly discuss the implications of this analysis to the problem of formation of topological defects in the early universe.

scholarly journals Origins of mass

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Frank Wilczek
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Hadron Collider ◽  
Z Bosons ◽  
Back Reaction ◽  
Higgs Particle ◽  
Mass Generation ◽  
Gauge Symmetries ◽  
High Degree

AbstractNewtonian mechanics posited mass as a primary quality of matter, incapable of further elucidation. We now see Newtonian mass as an emergent property. That mass-concept is tremendously useful in the approximate description of baryon-dominated matter at low energy — that is, the standard “matter” of everyday life, and of most of science and engineering — but it originates in a highly contingent and non-trivial way from more basic concepts. Most of the mass of standard matter, by far, arises dynamically, from back-reaction of the color gluon fields of quantum chromodynamics (QCD). Additional quantitatively small, though physically crucial, contributions come from the intrinsic masses of elementary quanta (electrons and quarks). The equations for massless particles support extra symmetries — specifically scale, chiral, and gauge symmetries. The consistency of the standard model relies on a high degree of underlying gauge and chiral symmetry, so the observed non-zero masses of many elementary particles (W and Z bosons, quarks, and leptons) requires spontaneous symmetry breaking. Superconductivity is a prototype for spontaneous symmetry breaking and for mass-generation, since photons acquire mass inside superconductors. A conceptually similar but more intricate form of all-pervasive (i.e. cosmic) superconductivity, in the context of the electroweak standard model, gives us a successful, economical account of W and Z boson masses. It also allows a phenomenologically successful, though profligate, accommodation of quark and lepton masses. The new cosmic superconductivity, when implemented in a straightforward, minimal way, suggests the existence of a remarkable new particle, the so-called Higgs particle. The mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter. Earlier results suggested, and recent observations at the Large Hadron Collider (LHC) may indicate, the actual existence of the Higgs particle, with mass m H ≈ 125 GeV. In addition to consolidating our understanding of the origin of mass, a Higgs particle with m H ≈ 125 GeV could provide an important clue to the future, as it is consistent with expectations from supersymmetry.

scholarly journals THE HISTORY OF THE GURALNIK, HAGEN AND KIBBLE DEVELOPMENT OF THE THEORY OF SPONTANEOUS SYMMETRY BREAKING AND GAUGE PARTICLES

2009 ◽  
Vol 24 (14) ◽  
pp. 2601-2627 ◽  
Author(s):  
GERALD S. GURALNIK
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Solution Space ◽  
Quantum Field ◽  
Historical Material ◽  
Intrinsic Nonlinearity ◽  
History Of ◽  
Do So

I discuss historical material about the beginning of the ideas of spontaneous symmetry breaking and particularly the role of the paper by Guralnik, Hagen and Kibble in this development. I do so adding a touch of some more modern ideas about the extended solution-space of quantum field theory resulting from the intrinsic nonlinearity of nontrivial interactions.

scholarly journals Nonperturbative aspects of spontaneous symmetry breaking

2021 ◽  
Vol 36 (13) ◽  
pp. 2150074
Author(s):  
J. Gamboa ◽  
J. López-Sarrión
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
Scalar Quantum ◽  
Infrared Limit ◽  
Theory Formula

Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when [Formula: see text] (or infrared limit). In this infrared approximation the theory [Formula: see text] is formally two-dimensional and its Euclidean solutions are instantons. For BPST-like solutions with [Formula: see text], the map between [Formula: see text] in two dimensions and self-dual Yang–Mills theory is carefully discussed.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

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