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Symmetry
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Boundaries in Quantum Field Theories
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Boundaries in Quantum Field Theories

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

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 5483

Special Issue Editor

Prof. Dr. Nicola Maggiore

E-Mail Website
Guest Editor
Dipartimento di Fisica, Università di Genova, Genoa, ‎Italy
Interests: quantum field theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The role of boundaries is crucial in many aspects of quantum field theories. The first example which comes to mind might be the Casimir effect, which motivated Symanzik in 1981 to formulate a systematic way to introduce boundaries in QFTs. He translated the presence of a boundary by means of a condition on the propagators, which vanish if calculated for points lying on opposite sides of the boundary. A lot has changed since then. Think, for instance, of topological field theories, which do not have local degrees of freedom, the only observables being geometrical, global holes of the manifolds, knots, etc. These are theories linked to vanishing Hamiltonian, where fields have no particle interpretation. Nonetheless, when a boundary is introduced, topological field theories acquire a physical life: Quantum spin Hall states appear on the edge of three-dimensional topological Chern–Simons theory. Similarly, topological insulators are described by adding a boundary to topological three- and four-dimensional BF theories. The wild world of two-dimensional conformal field theories was tamed by Chern–Simons theory having a cylinder as a boundary. Another outstanding example is given by AdS/CFT correspondence, or gauge/gravity duality, where a gravity bulk theory with a charged Reissner–Nordström black hole on a d+1 AdS spacetime is dual to its d-dimensional boundary, which is where gauge field theory stems from. This correspondence allows computing correlators in the strong coupling regime by means of their higher dimensional weak coupled counterpart. Born in a string theory framework, this duality has found a spectacular realization in condensed matter physics, where strongly correlated materials are quite difficult, if not impossible, to study differently.

Prof. Dr. Nicola Maggiore
Guest Editor

Manuscript Submission Information

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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

  • quantum field theory
  • AdS/CFT
  • AdS/CMT
  • gauge/gravity
  • holography
  • edge states
  • quantum spin hall
  • topological insulators
  • boundary algebra
  • boundary conditions

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Published Papers (2 papers)

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Research

19 pages, 383 KiB  
Article
Boundary Conditions that Remove Certain Ultraviolet Divergences
by Roderich Tumulka
Symmetry 2021, 13(4), 577; https://doi.org/10.3390/sym13040577 - 31 Mar 2021
Cited by 1 | Viewed by 1888
Abstract
In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. [...] Read more.
In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves to determine the probability distribution of detection times and places on a time-like 3-surface. Full article
(This article belongs to the Special Issue Boundaries in Quantum Field Theories)
25 pages, 393 KiB  
Article
Holographic Projection of Electromagnetic Maxwell Theory
by Erica Bertolini and Nicola Maggiore
Symmetry 2020, 12(7), 1134; https://doi.org/10.3390/sym12071134 - 7 Jul 2020
Cited by 8 | Viewed by 3050
Abstract
The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-Moody algebra formed by a [...] Read more.
The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-Moody algebra formed by a subset of the bulk fields is obtained with central charge proportional to the inverse of the Maxwell coupling constant, and the degrees of freedom of the boundary theory are identified as two vector fields, also suggesting that the 3D theory should be a gauge theory. Finally the holographic contact between bulk and boundary theory is reached in two inequivalent ways, both leading to a unique 3D action describing a new gauge theory of two coupled vector fields with a topological Chern-Simons term with massive coefficient. In order to check that the 3D projection of 4D Maxwell theory is well defined, we computed the energy-momentum tensor and the propagators. The role of discrete symmetries is briefly discussed. Full article
(This article belongs to the Special Issue Boundaries in Quantum Field Theories)
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