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.

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. 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.

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 De Sitter braneworld and gravitational waves

2021 ◽  
Author(s):  
Dong-Yu Li ◽  
Zhao-Xiang Wu ◽  
Hao Hu ◽  
Bao-Min Gu
Keyword(s):  
Gravitational Waves ◽  
Scalar Fields ◽  
Background Solution ◽  
De Sitter ◽  
Dimensional Theory ◽  
Massive Mode ◽  
Large Extra Dimension ◽  
Mass Gap ◽  
Massless Mode ◽  
Background Fields

We study the braneworld theory constructed by multi scalar fields. The model contains a smooth and infinitely large extra dimension, allowing the background fields propagating in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of massless mode evolve the same as the four dimensional theory, while that of the massive modes evolve greatly different from the massless mode.

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.

scholarly journals HYPER-KÄHLER METRICS BUILDING AND INTEGRABLE MODELS

1994 ◽  
Vol 09 (34) ◽  
pp. 3163-3173 ◽  
Author(s):  
E.H. SAIDI ◽  
M.B. SEDRA
Keyword(s):  
Integrable Systems ◽  
Constraint Equation ◽  
Integrable Models ◽  
Explicit Solutions ◽  
Harmonic Superspace ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Conserved Currents

Methods developed for the analysis of integrable systems are used to study the problem of hyper-Kähler metrics building as formulated in D=2, N=4 supersymmetric harmonic superspace. We show in particular that the constraint equation [Formula: see text] and its Toda-like generalizations are integrable. Explicit solutions together with the conserved currents generating the symmetry responsible for the integrability of these equations are given. Other features are also discussed.

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.

scholarly journals Gauge from Holography and Holographic Gravitational Observables

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
José A. Zapata
Keyword(s):  
Null Space ◽  
Homology Class ◽  
Gauge Invariant ◽  
Gauge Equivalence ◽  
Lagrangian Field Theory ◽  
Conserved Current ◽  
Local Observables ◽  
Two Sides ◽  
Conserved Currents ◽  
Dimensional Surface

In a spacetime divided into two regions U1 and U2 by a hypersurface Σ, a perturbation of the field in U1 is coupled to perturbations in U2 by means of the holographic imprint that it leaves on Σ. The linearized gluing field equation constrains perturbations on the two sides of a dividing hypersurface, and this linear operator may have a nontrivial null space. A nontrivial perturbation of the field leaving a holographic imprint on a dividing hypersurface which does not affect perturbations on the other side should be considered physically irrelevant. This consideration, together with a locality requirement, leads to the notion of gauge equivalence in Lagrangian field theory over confined spacetime domains. Physical observables in a spacetime domain U can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that ∂Σ⊂∂U. The set of observables of this type is sufficient to distinguish gauge inequivalent solutions. The integral of a conserved current on a hypersurface is sensitive only to its homology class [Σ], and if U is homeomorphic to a four ball the homology class is determined by its boundary S=∂Σ. We will see that a result of Anderson and Torre implies that for a class of theories including vacuum general relativity all local observables are holographic in the sense that they can be written as integrals of over the two-dimensional surface S. However, nonholographic observables are needed to distinguish between gauge inequivalent solutions.

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.

scholarly journals Spontaneous symmetry breaking and Nambu–Goldstone modes in open classical and quantum systems

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Yoshimasa Hidaka ◽  
Yuki Minami
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Type A ◽  
Quantum Systems ◽  
Propagation Mode ◽  
Goldstone Mode ◽  
Type B ◽  
Goldstone Theorem ◽  
Diffusion Type ◽  
Goldstone Modes

Abstract We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu–Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward–Takahashi identity and the effective action formalism, we establish the Nambu–Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu–Goldstone modes. Using these coefficients, we classify the Nambu–Goldstone modes into four types: type-A propagation, type-A diffusion, type-B propagation, and type-B diffusion modes.

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