PP.LB03.05

Strocchi, Enrico; Vitali, Francesca; Rosticci, Martina; Rinaldi, E; Cicero, Arrigo Francesco Giuseppe; Malini, Pier Luigi; Borghi, Claudio

doi:10.1097/01.hjh.0000469023.09622.95

Cited by 1 publication

(8 citation statements)

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“…Before embarking to gauge symmetries, it is quite helpful to reconsider global symmetries. Also here a full field-theoretical treatment [30] leads to insights which seem at first counter-intuitive. But in the end, they give a much clearer notion of what symmetry (breaking) at the quantum level really is.…”

Section: Global Symmetriesmentioning

confidence: 94%

“…It should be noted that most of the following depends strongly on the space-time dimension. In particular, most mechanisms do not operate at the quantum level in one and two dimensions [30,31], due to infrared fluctuations. This the celebrated Coleman-Mermin-Wagner theorem [30,32,33].…”

Section: Global Symmetriesmentioning

confidence: 99%

“…In particular, most mechanisms do not operate at the quantum level in one and two dimensions [30,31], due to infrared fluctuations. This the celebrated Coleman-Mermin-Wagner theorem [30,32,33]. In the following it will always be implicitly assumed that the dimensionality is sufficient, i. e. usually three or more, to allow for the described phenomena to take place.…”

Section: Global Symmetriesmentioning

confidence: 99%

“…One 10 of the most remarkable consequences of spontaneous symmetry breaking is the masslessness of one of the degrees of freedom in (23). This is a special case of Goldstone's theorem [14,30,50]. It is useful to formulate this theorem more generally, both at the classical and quantum level, to fully appreciate how the situation in the metastable case differs.…”

Section: The Goldstone Theoremmentioning

confidence: 99%

“…It remains to understand what happens in the metastable case 12 . Because the vacuum expectation value in equation (30) explicitly vanishes, the equation is already fulfilled without a zero of the inverse propagator. Thus, the same argument for the presence of massless poles can no longer be made.…”

Section: Metastable Casementioning

confidence: 99%

See 4 more Smart Citations

Brout–Englert–Higgs physics: From foundations to phenomenology

Maas

2019

Progress in Particle and Nuclear Physics

107

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Brout-Englert Higgs physics is one of the most central and successful parts of the standard model. It is also part of a multitude of beyond-the-standard-model scenarios.The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the Brout-Englert-Higgs effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram of theories with elementary Higgs fields and gauge interactions.The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Fröhlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory in this framework. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gaugedependent, elementary states of the Higgs and W -bosons and Z-boson, but also of the elementary fermions, is adequate and successful.These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms.In this course it will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed.Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included. If there is no gauge-invariant way of defining the vacuum expectation value of the Higgs, the whole standard procedure [14] of doing BEH physics seems to collapse on itself at first. This seems to question the whole basis of the current theoretical description of experiments, despite its huge success [10]. But it does not. Rather, it can be shown that a treatment taking the gauge-dependence into account will lead to, essentially, the same results for the standard model.How this works out is exactly the core of this review: The construction of a fully gauge-invariant description of this physics, and how the standard phenomenology follows from it. This starts in section 3. There, a gauge-invariant description of the theory (3) will be set up. This is the first step of developing a comprehensive, field-theoretical consistent view on BEH physics. This view is continued by establis...

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Section: Global Symmetriesmentioning

confidence: 94%