Structures of conserved currents and mass spectra for scalar fields. III. Current classification scheme in terms of Killing equations and the Goldstone theorem

1981 ◽  
Vol 59 (11) ◽  
pp. 1680-1681
Author(s):  
Meiun Shintani
Keyword(s):  
Mass Spectra ◽  
Classification Scheme ◽  
Goldstone Boson ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Goldstone Theorem ◽  
Scalar Particles ◽  
Conformally Invariant ◽  
Conserved Currents ◽  
Killing Equations

We present a new classification scheme for the currents Jμ(x) = Qμν(x)Cν(x) in terms of the solutions of the Killing equations for Cμ(x). The new scheme enables us to treat any coordinate transformations (e.g., special conformal transformations), and to discuss the mass spectra for the scalar particles in a conformally-invariant system. Moreover, with the aid of the generalized Goldstone theorem exploited in the previous article under the same title, we shall point out the nonexistence of the Goldstone boson with regard to the special conformal transformations.

Structures of conserved currents and mass spectra for scalar fields: an approach to the generalization of the Goldstone theorem

1980 ◽  
Vol 58 (4) ◽  
pp. 463-471
Author(s):  
Meiun Shintani
Keyword(s):  
Mass Spectrum ◽  
Scalar Field ◽  
Mass Spectra ◽  
Vacuum State ◽  
Scalar Fields ◽  
Goldstone Theorem ◽  
Massive Mode ◽  
Conserved Current ◽  
Conserved Currents ◽  
A Current

Considering the commutators between a scalar field and a conserved current, we shall clarify the connection between the mass spectrum for a scalar field and the structures of a current. For a special form of currents involving c-number functions, non-invariance of the vacuum under the corresponding transformation entails the existence of a massive mode. It is shown that once a type of currents is specified, the pole structures for [Formula: see text] depend only on c-number parts of Jμ(x). We shall show that the non-vanishing Goldstone commutator does not automatically imply the degeneracy of the vacuum state, and discuss the applicability of the Goldstone theorem.

Structures of conserved currents and mass spectra for scalar fields. II. A covariant formulation of the generalization of the Goldstone theorem

1980 ◽  
Vol 58 (6) ◽  
pp. 763-767
Author(s):  
Meiun Shintani
Keyword(s):  
Mass Spectra ◽  
Constraint Equation ◽  
Scalar Fields ◽  
Covariant Formulation ◽  
Goldstone Theorem ◽  
Massive Mode ◽  
Key Equation ◽  
Conserved Current ◽  
Goldstone Modes ◽  
Conserved Currents

By adding the constraint equation [Formula: see text] on the generator G to our formulation exploited in the previous article under the same title (M. Shintani, Can. J. Phys. 58, 463 (1980)), we present a Lorentz-covariant approach to the generalized Goldstone theorem which applies even when the conserved current involves non-trivial c-number functions. As a result of the constraint equation, we derive a new key equation. By solving a new key equation together with the other key equations already obtained in the first part of this series, we can eliminate the massive mode and extract only the Goldstone modes. It is shown that any generator is either a relevant generator or an irrelevant one.

scholarly journals Several Physical Properties of Two Interacting Complex Scalar Fields at Finite Density

2011 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Tran Huu Phat ◽  
Phan Thi Duyen
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Meissner Effect ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Goldstone Theorem ◽  
Complex Scalar ◽  
Finite Density ◽  
Chemical Potentials ◽  
The Mean

The two interacting complex scalar fields at finite density is considered in the mean field approximation. It is shown that although the symmetry is spontaneously broken for the chemical potentials bigger than the meson masses in vacuum, but the Goldstone theorem is not preserved in broken phase. Then two mesons are condensed and their condensates turn out to be two-gap superconductor which is signaled by the appearance of the Meissner effect as well as the Abrikosov and non-Abrikosov vortices. Finally, there exhibits domain wall which is the plane, where two condensates flowing in opposite directions collide and generate two types of vortices with cores in the wall.

scholarly journals On Mass Spectra of Primordial Black Holes

2021 ◽  
Vol 8 ◽  
Author(s):  
Alexander A. Kirillov ◽  
Sergey G. Rubin
Keyword(s):  
Black Holes ◽  
Mass Spectrum ◽  
Mass Spectra ◽  
Scalar Fields ◽  
Small Mass ◽  
Primordial Black Holes ◽  
Classical Motion ◽  
Multiple Production ◽  
Analytical Formulas ◽  
Intrinsic Feature

Evidence for the primordial black holes (PBH) presence in the early Universe renews permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known models is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is the multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage. Analytical formulas have been developed that contain both quantum and classical contributions.

Higher spin conserved currents in c = 1 conformally invariant systems

1988 ◽  
Vol 300 ◽  
pp. 637-657 ◽  
Author(s):  
M. Baake ◽  
P. Christe ◽  
V. Rittenberg
Keyword(s):  
Conformally Invariant ◽  
Higher Spin ◽  
Conserved Currents

scholarly journals Conserved Currents in Supersymmetric Quantum Cosmology?

1997 ◽  
Vol 06 (05) ◽  
pp. 625-641 ◽  
Author(s):  
P. V. Moniz
Keyword(s):  
Differential Equations ◽  
Quantum Cosmology ◽  
Scalar Fields ◽  
Square Root ◽  
Root Structure ◽  
Complex Scalar ◽  
First Order ◽  
Class A ◽  
Conserved Currents ◽  
First Order Differential Equations

In this paper we investigate whether conserved currents can be sensibly defined in super-symmetric minisuperspaces. Our analysis deals with k = +1 FRW and Bianchi class-A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The "square-root" structure of N = 1 super-gravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, equations of the type ∇a Ja = 0 may only be obtained from Wheeler–DeWittlike equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In Appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle–Hawking state can now be satisfactorily identified. In Appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.

Symmetry breaking in conformal Einstein–Hilbert action

2015 ◽  
Vol 93 (11) ◽  
pp. 1352-1355
Author(s):  
M.R. Tanhayi ◽  
S. Ejlali
Keyword(s):  
Symmetry Breaking ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Space Time ◽  
Massless Scalar ◽  
Conformally Invariant ◽  
Free Theory ◽  
Massless Spin ◽  
Background Space ◽  
Hilbert Action

In this paper, we study the conformal symmetry breaking in conformally invariant Hilbert–Einstein action via expansion of action up to second order around the background space–time. It is shown that the theory can be described a non-tachyonic and ghost-free theory that propagates massless spin-2, massive gauge, and also massless scalar fields.

scholarly journals Gravitationally coupled magnetic monopole and conformal symmetry breakingThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 251-254 ◽  
Author(s):  
Ariel Edery ◽  
Luca Fabbri ◽  
M. B. Paranjape
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Magnetic Monopoles ◽  
De Sitter ◽  
Long Distance ◽  
Abelian Gauge ◽  
Conformally Invariant ◽  
The Core

We consider a Georgi–Glashow model conformally coupled to gravity. The conformally invariant action includes a triplet of scalar fields and SO(3) non-Abelian gauge fields. However, the usual mass term μ2ϕ2 is forbidden by the symmetry, and this role is now played by the conformal coupling of the Ricci scalar to the scalar fields. Spontaneous symmetry breaking occurs via gravitation. The spherically symmetric solutions correspond to localized solitons (magnetic monopoles) in asymptotically anti-de Sitter (AdS) spacetime and the metric outside the core of the monopole is found to be Schwarzschild–AdS. Though conformal symmetry excludes the Einstein–Hilbert term in the original action, it emerges in the effective action after spontaneous symmetry breaking and dominates the low-energy–long-distance regime outside the core of the monopole.

My Life as a Boson: The Story of "The Higgs"

2012 ◽  
Vol 01 (02) ◽  
pp. 50-51
Author(s):  
Peter Higgs
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Landau Theory ◽  
Scalar Fields ◽  
Bcs Theory ◽  
Goldstone Theorem ◽  
Ginzburg Landau ◽  
Goldstone Bosons ◽  
Massless Spin ◽  
The Subject

The story begins in 1960, when Nambu, inspired by the BCS theory of superconductivity, formulated chirally invariant relativistic models of interacting massless fermions in which spontaneous symmetry breaking generates fermionic masses (the analogue of the BCS gap). Around the same time Jeffrey Goldstone discussed spontaneous symmetry breaking in models containing elementary scalar fields (as in Ginzburg-Landau theory). I became interested in the problem of how to avoid a feature of both kinds of model, which seemed to preclude their relevance to the real world, namely the existence in the spectrum of massless spin-zero bosons (Goldstone bosons). By 1962 this feature of relativistic field theories had become the subject of the Goldstone theorem.

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