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Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof....
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Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 14635

Special Issue Editors

Prof. Dr. Sergei D. Odintsov

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Guest Editor
ICREA, P. Lluis Companyas 23, 08010 Barcelona and Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193 Barcelona, Spain
Interests: cosmology; dark energy and inflation; quantum gravity; modified gravity and beyond general relativity; quantum fields at external fields
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Eduardo Guendelman

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Guest Editor
Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel
Interests: gravity; cosmology; particle physics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Kimball Milton

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Guest Editor
Homer L. Dodge Department of Physics and Astronomy, Nielsen Hall 325, The University of Oklahoma, Norman, OK 73019-2061, USA
Interests: High energy theory; quantum field theory; Casimir effect

Special Issue Information

Dear Colleagues,

This Special Issue in Symmetry devoted to high-energy physics, cosmology, and gravitation, as a Memorial for Prof. Steven Weinberg.             

Steven Weinberg (May 3, 1933–July 23, 2021), was a Nobel laureate in physics for his model of the unification of electromagnetism and nuclear weak forces, with the masses of the force-carriers of the weak part of the interaction being explained by spontaneous symmetry breaking. One of the model’s fundamental aspects was the prediction of the existence of the Higgs boson. Weinberg's model, now known as the electroweak unification theory, had the same symmetry structure as that proposed by Glashow in 1961: both included a then-unknown component of the weak interaction mechanism between leptons, known as the  neutral current interaction, which was mediated by the Z boson. The 1973 experimental discovery of weak neutral currents was one verification of the electroweak theory; the Z boson itself was discovered a decade later. The paper by Weinberg in which he presented this theory is now one of the most cited works ever in high-energy physics, although it was not cited at all until four years after publication, subsequent to the work of ‘t Hooft and Veltman, who showed it was renormalizable. Weinberg also contributed significantly to cosmology, including the cosmological constant problem, and wrote famous books on gravitation. His work on effective and phenomenological Lagrangians was and remains particularly influential. 

In this Special Issue we want to invite contributions on the subjects developed by Steven Weinberg; personal recollections by people close to him are also welcomed. As is apparent, Weinberg covered all the primary areas of active work at present on fundamental physics, so we welcome contributions in gravity, cosmology, particle physics phenomenology, supersymmetry, and string theory. In the work of Weinberg, the notion of symmetry—in particular gauge symmetry and symmetry breaking—was of particular importance, so we encourage related contributions, including symmetry breaking, etc. Symmetry is naturally the main subject being promoted in the Symmetry journal. Therefore, we want to honor the memory of one the most important physicists of our time and provide perspectives for the future of fundamental physics as seen by the different contributors. 

Prof. Dr. Sergei D. Odintsov
Prof. Dr. Eduardo Guendelman
Prof. Dr. Kimball Milton
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (7 papers)

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Research

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24 pages, 534 KiB  
Article
Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe
by Alexander Balakin, Alexei Ilin and Amir Shakirzyanov
Symmetry 2023, 15(10), 1824; https://doi.org/10.3390/sym15101824 - 26 Sep 2023
Cited by 2 | Viewed by 1114
Abstract
We consider an isotropic homogeneous cosmological model with five interacting elements: first, the dynamic aether presented by a unit timelike vector field; second, the pseudoscalar field describing an axionic component of the dark matter; third, the cosmic dark energy, described by a rheologic [...] Read more.
We consider an isotropic homogeneous cosmological model with five interacting elements: first, the dynamic aether presented by a unit timelike vector field; second, the pseudoscalar field describing an axionic component of the dark matter; third, the cosmic dark energy, described by a rheologic fluid; fourth, the non-axionic dark matter coupled to the dark energy; and fifth, the gravity field. We show that the early evolution of the Universe described by this model can include two specific epochs: the first one can be characterized as a super-inflation epoch; the second epoch is associated with an oscillatory regime. The dynamic aether carries out a regulatory mission; the rheologic dark fluid provides the specific features of the spacetime evolution. The oscillations of the scale factor and of the Hubble function are shown to switch on the parametric (Floquet-type) mechanism of the axion number growth. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
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25 pages, 423 KiB  
Article
String Theory Bounds on the Cosmological Constant, the Higgs Mass, and the Quark and Lepton Masses
by Per Berglund, Tristan Hübsch and Djordje Minic
Symmetry 2023, 15(9), 1660; https://doi.org/10.3390/sym15091660 - 28 Aug 2023
Cited by 2 | Viewed by 1250
Abstract
In this paper, we elaborate on the new understanding of the cosmological constant and the gauge hierarchy problems in the context of string theory in its metastring formulation, based on the concepts of modular spacetime and Born geometry. The interplay of phase space [...] Read more.
In this paper, we elaborate on the new understanding of the cosmological constant and the gauge hierarchy problems in the context of string theory in its metastring formulation, based on the concepts of modular spacetime and Born geometry. The interplay of phase space (and Born geometry), the Bekenstein bound, the mixing between ultraviolet (UV) and infrared (IR) physics and modular invariance in string theory is emphasized. This new viewpoint is fundamentally rooted in quantum contextuality and not in statistical observer bias (anthropic principle). We also discuss the extension of this point of view to the problem of masses of quarks and leptons and their respective mixing matrices. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
12 pages, 309 KiB  
Article
Big Steve and the State of the Universe
by Richard P. Woodard
Symmetry 2023, 15(4), 856; https://doi.org/10.3390/sym15040856 - 3 Apr 2023
Cited by 3 | Viewed by 1331
Abstract
I share some reminiscences of the late Steven Weinberg. Then I discuss a topic in quantum field theory that he taught me: the role of state wave functionals in deriving the iϵ term of the Feynman propagator when using functional formalism. This [...] Read more.
I share some reminiscences of the late Steven Weinberg. Then I discuss a topic in quantum field theory that he taught me: the role of state wave functionals in deriving the iϵ term of the Feynman propagator when using functional formalism. This is perhaps a curiosity for in–out scattering amplitudes on flat-space backgrounds, but it has much greater significance for the in–in amplitudes of the Schwinger–Keldysh formalism in cosmology. It also touches on the fate, about which Weinberg wondered, of the large logarithms one sometimes finds in quantum corrections from inflationary particle production. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
11 pages, 297 KiB  
Article
Momentum Gauge Fields and Non-Commutative Space–Time
by Eduardo Guendelman and Douglas Singleton
Symmetry 2023, 15(1), 126; https://doi.org/10.3390/sym15010126 - 2 Jan 2023
Cited by 9 | Viewed by 1548
Abstract
In this work, we present a gauge principle that starts with the momentum space representation of the position operator (x^i=iℏ∂∂pi), rather than starting with the position space representation of the momentum operator [...] Read more.
In this work, we present a gauge principle that starts with the momentum space representation of the position operator (x^i=iℏ∂∂pi), rather than starting with the position space representation of the momentum operator (p^i=−iℏ∂∂xi). This extension of the gauge principle can be seen as a dynamical version of Born’s reciprocity theory, which exchanges position and momentum. We discuss some simple examples with this new type of gauge theory: (i) analog solutions from ordinary gauge theory in this momentum gauge theory, (ii) Landau levels using momentum gauge fields, and (iii) the emergence of non-commutative space–times from the momentum gauge fields. We find that the non-commutative space–time parameter can be momentum dependent, and one can construct a model where space–time is commutative at low momentum, but becomes non-commutative at high momentum. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
15 pages, 328 KiB  
Article
Weinberg’s Compositeness
by Ubirajara van Kolck
Symmetry 2022, 14(9), 1884; https://doi.org/10.3390/sym14091884 - 9 Sep 2022
Cited by 17 | Viewed by 1839
Abstract
Nearly 60 years ago, Weinberg suggested a criterion for particle “compositeness”, which has acquired a new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg’s [...] Read more.
Nearly 60 years ago, Weinberg suggested a criterion for particle “compositeness”, which has acquired a new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg’s creations, the model-independent framework of effective field theories. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
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Review

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15 pages, 365 KiB  
Review
Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview
by Sergei D. Odintsov, Vasilis K. Oikonomou and Ratbay Myrzakulov
Symmetry 2022, 14(4), 729; https://doi.org/10.3390/sym14040729 - 3 Apr 2022
Cited by 52 | Viewed by 3744
Abstract
In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects [...] Read more.
In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter aM, which we calculate for the cases of f(R,ϕ) gravity, Chern–Simons-corrected f(R,ϕ) gravity, Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity. The exact form of aM is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for aM expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
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Other

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7 pages, 232 KiB  
Obituary
Memories of Steven Weinberg (1933–2021)
by Paul H. Frampton
Symmetry 2022, 14(3), 488; https://doi.org/10.3390/sym14030488 - 28 Feb 2022
Viewed by 2037
Abstract
Steven Weinberg, renowned particle theorist and Nobel laureate, passed away in July 2021. We discuss selections of his work on effective field theory, electroweak unification, and symmetry related topics. We then add a few memories of Weinberg at Harvard University then at the [...] Read more.
Steven Weinberg, renowned particle theorist and Nobel laureate, passed away in July 2021. We discuss selections of his work on effective field theory, electroweak unification, and symmetry related topics. We then add a few memories of Weinberg at Harvard University then at the University of Texas, Austin. Full article
(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)
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