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Symmetry
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Geometry and Symmetry in Quantum Field Theory
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Geometry and Symmetry in Quantum Field Theory

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

Deadline for manuscript submissions: closed (21 November 2021) | Viewed by 4180

Special Issue Editors

Prof. Dr. Annalisa Marzuoli

E-Mail
Guest Editor
1. Dipartimento di Matematica ‘F Casorati’, Università di Pavia, Pavia, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Bari, Italy
Prof. Dr. Song He

E-Mail Website
Guest Editor
Center for Theoretical Physics and College of Physics, Jilin University, Changchun 130022, China
Interests: quantum field theory; string theory; mathematical physics

Special Issue Information

Dear colleagues,

When dealing with contemporary aspects of the interplay between Geometry and Quantum Field Theory, there is a high risk of flattening the multifaceted profile of this topic. However, in order to set limits to the scope of this Special Issue, the focal point will be topological QFT, the Chern–Simons–Witten model as a prototype and a shared source of inspiration for the contributions. 

A (non-exhaustive) list of models, approaches, and methods includes: (gauge) QFT on non-commutative spaces and spacetimes; induced boundary models; q-deformed symmetries and supersymmetry; canonical quantization schemes in QFT; BV and BFV formalisms; discretized models; cosmological and black hole solutions; topological invariants of knots and 3-manifolds. 

The last decade has seen a flourishing of applications of tools from (Chern–Simons and BF) TQFT to condensed matter physics (effective actions in 2d Hall materials and graphene, topological insulators in 2d and 3d) also in connection with the search for theoretical schemes and practical implementations of topological quantum computing. 

Fostering research in the foundational topics therefore appears more compelling than ever.

text

Figure: courtesy of Mauro Carfora

Prof. Dr. Annalisa Marzuoli
Prof. Dr. Song He
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.

Keywords

  • Chern–Simons (super)gravity models
  • WZW and boundary theories
  • BV and BFV formalisms
  • q-deformed symmetries
  • Supergeometry
  • Topological and combinatorial invariants

Published Papers (2 papers)

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Research

26 pages, 486 KiB  
Article
Topological and Dynamical Aspects of Jacobi Sigma Models
by Francesco Bascone, Franco Pezzella and Patrizia Vitale
Symmetry 2021, 13(7), 1205; https://doi.org/10.3390/sym13071205 - 5 Jul 2021
Cited by 1 | Viewed by 1401
Abstract
The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories—recently introduced by the authors—which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and [...] Read more.
The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories—recently introduced by the authors—which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and finite dimension of the reduced phase space. After reviewing the main novelties and peculiarities of these models, we perform a detailed analysis of constraints and ensuing gauge symmetries in the Hamiltonian approach. Contact manifolds as well as locally conformal symplectic manifolds are discussed, as main instances of Jacobi manifolds. Full article
(This article belongs to the Special Issue Geometry and Symmetry in Quantum Field Theory)
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13 pages, 303 KiB  
Article
Unconventional SUSY and Conventional Physics: A Pedagogical Review
by Pedro D. Alvarez, Lucas Delage, Mauricio Valenzuela and Jorge Zanelli
Symmetry 2021, 13(4), 628; https://doi.org/10.3390/sym13040628 - 9 Apr 2021
Cited by 12 | Viewed by 2147
Abstract
In supersymmetric extensions of the Standard Model, the observed particles come in fermion–boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to [...] Read more.
In supersymmetric extensions of the Standard Model, the observed particles come in fermion–boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY’s predictive power and it is unclear whether SUSY, in its standard form, can help reducing the remaining puzzles of the standard model (SM). Here we argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this unconventional representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields and SUSY is not a fully off-shell invariance of the action. The resulting systems are remarkably simple, closely resembling a standard quantum field theory and SUSY still emerges as a contingent symmetry that depends on the features of the vacuum/ground state. We illustrate the general construction with two examples: (i) A 2 + 1 dimensional system based on the osp(2,2|2) superalgebra, including Lorentz and u(1) generators that describe graphene; (ii) a supersymmetric extension of 3 + 1 conformal gravity with an SU(2,2|2) connection that describes a gauge theory with an emergent chiral symmetry breaking, coupled to gravity. The extensions to higher odd and even dimensions, as well as the extensions to accommodate more general internal symmetries are also outlined. Full article
(This article belongs to the Special Issue Geometry and Symmetry in Quantum Field Theory)
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