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

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

Deadline for manuscript submissions: closed (30 April 2020).

Special Issue Editor

Dr. Claudio Cremaschini

Guest Editor
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

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Keywords

  • 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 (6 papers)

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Research

Open AccessArticle
Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time
Symmetry 2020, 12(4), 531; https://doi.org/10.3390/sym12040531 - 03 Apr 2020
Cited by 2
Abstract
Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic [...] Read more.
Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out. Full article
Open AccessArticle
The Wave-Front Equation of Gravitational Signals in Classical General Relativity
Symmetry 2020, 12(2), 216; https://doi.org/10.3390/sym12020216 - 02 Feb 2020
Abstract
In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015–2019). The Hamilton–Jacobi equation [...] Read more.
In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015–2019). The Hamilton–Jacobi equation obtained in this way yields a wave-front description of gravitational field dynamics. It is shown that on a suitable subset of configuration space the latter equation reduces to a Klein–Gordon type equation associated with a 4-scalar field which identifies the wave-front surface of a gravitational signal. Its physical role and mathematical interpretation are discussed. Radiation-field wave-front solutions are pointed out, proving that according to this description, gravitational wave-fronts propagate in a given background space-time as waves characterized by the invariant speed-of-light c. The outcome is independent of the actual shape of the same wave-fronts and includes the case of gravitational waves which are characterized by an eikonal representation and propagate in a generic curved space-time along a null geodetics. The same waves are shown: (a) to correspond to the geometric-optics limit of the same curved space-time solutions; (b) to propagate in a flat space-time as plane waves with constant amplitude; (c) to display also the corresponding form of the wave-front in curved space-time. The result is consistent with the theory of the linearized Einstein field equations and the existence of gravitational waves achieved in such an asymptotic regime. Consistency with the non-linear Trautman boundary-value theory is also displayed. Full article
Open AccessFeature PaperArticle
Noether’s Theorem in Non-Local Field Theories
Symmetry 2020, 12(1), 35; https://doi.org/10.3390/sym12010035 - 23 Dec 2019
Abstract
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincaré group in field theories with higher-order derivatives and in non-local field theories. We consider an example [...] Read more.
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincaré group in field theories with higher-order derivatives and in non-local field theories. We consider an example of non-local charged scalar field equations with broken C (charge conjugation) and CPT (charge conjugation, parity, and time reversal) symmetries. For this case, we find simple analytical expressions for the conserved currents. Full article
Open AccessArticle
Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time
Symmetry 2019, 11(11), 1413; https://doi.org/10.3390/sym11111413 - 15 Nov 2019
Abstract
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended [...] Read more.
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter ϰ introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection. Full article
Open AccessArticle
Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy
Symmetry 2019, 11(7), 860; https://doi.org/10.3390/sym11070860 - 02 Jul 2019
Cited by 1
Abstract
A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations [...] Read more.
A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a two-dimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the Klein–Gordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered. Full article
Open AccessArticle
Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity
Symmetry 2019, 11(4), 592; https://doi.org/10.3390/sym11040592 - 24 Apr 2019
Cited by 2
Abstract
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
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