Special Issue "Space-Time and Symmetry Properties: Classical and Quantum Descriptions"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 30 November 2019

Special Issue Editor

Guest Editor
Dr. Claudio Cremaschini

Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech Republic
Interests: general relativity; quantum gravity; quantum field theory; statistical physics; kinetic theories; plasma physics

Special Issue Information

Dear Colleagues,

The understanding of the geometrical structure of space–time via continuum or discrete representations poses challenging conceptual physical and mathematical questions. The goal of this Special Issue is to focus, in particular, on the small and large-scale geometrical/physical properties of space-time and its symmetry features, to motivate the investigation of a number of related topics arising both in the framework of the Einstein classical theory of General Relativity as well as among candidate theories of quantum gravity. These topics will concern in particular:

  • The space–time transformation properties with respect to the group of local point, i.e., coordinate, transformations and the consistency of current realizations adopted for classical and quantum gravity theories with respect to the principle of manifest covariance. The issue pertains both the identification of the classical Hamiltonian and Hamilton-Jacobi structures of General Relativity, as well as corresponding prescription of the physical postulates at the basis of a quantum mechanical description of space-time and canonical quantization.
  • The symmetry properties of space-time related to the emergent gravity phenomenon, whereby certain physical observables/characteristics of classical General Relativity follow from quantum gravity theory. These concern both the prescription of the local-coordinate value of the space-time metric tensor, via a suitable quantum expectation value, as well as the establishment of the very functional form of the General Relativity field equations.
  • Trajectory-based dynamics of classical and quantum gravitational field and statistical foundations of quantum space-time dynamics, including validity of Heisenberg inequalities, thermodynamical characterization and entropic principles.

Contributing papers addressing the issues mentioned above are welcome.

Dr. Claudio Cremaschini
Guest Editor

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 papers will be 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 1400 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.


  • Space-time local-point transformations and manifest covariance principle
  • Hamiltonian structure of space-time and variational formulation of General Relativity
  • Hamiltonian and Hamilton-Jacobi canonical quantization of classical gravity: continuum vs discrete space-time configurations
  • Trajectory-based representation of quantum space-time dynamics and emergent gravity phenomenon
  • Statistical characterization of quantum gravity field and implications on space-time symmetry properties

Published Papers (1 paper)

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Open AccessArticle
Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity
Symmetry 2019, 11(4), 592; https://doi.org/10.3390/sym11040592
Received: 17 February 2019 / Revised: 18 April 2019 / Accepted: 19 April 2019 / Published: 24 April 2019
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The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous [...] Read more.
The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder–Weyl variational formulation (2015–2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g μ ν being realized by the third-order 4-tensor Π μ ν α . It is shown that this generates a corresponding Hamilton–Jacobi theory in which the Hamilton principal function is a 4-tensor S α . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton–Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field. Full article

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Symmetries in Adaptive Networks
Authors: Eckehard Schöll, Rico Berner, Serhiy Yanchuk
Affiliation: Institute of Theoretical Physics, Technische Universität Berlin, Germany; (E.S.), (R.B.), (S.Y.)

Title: Bijective Analysis of Symmetry in Physics
Author: Srečko Šorli Amrit
Affiliation: Foundations of Physics Institute, Idrija, Slovenia

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