arXiv subjects

D. Vasak

Publications and source records attributed to D. Vasak.

7 recordsLinked to original sources

arXiv2023

On CCGG, the De Donder-Weyl Hamiltonian formulation of canonical gauge gravity

This paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder-Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical transformation theory. That framework derives, from a few basic physical and mathematical assumptions, equations describing generic matter and gravity dynamics with the spin connection emerging as a Yang Mills-type gauge field. While the interaction of any matter field with spacetime is fixed just by the transformation property of that field, a concrete gravity ansatz is introduced by the choice of the free (kinetic) gravity Hamiltonian. The key elements of this approach are discussed and its implications for particle dynamics and cosmology presented. Among the results are especially: - Anomalous Pauli coupling of spinors to curvature and torsion of spacetime, - spacetime with (A)dS ground state, inertia, torsion and geometrical vacuum energy, - Zero-energy balance of the Universe leading to a vanishing cosmological constant and torsional dark energy.

gr-qc↗

arXiv2022

Identity for scalar-valued functions of tensors and its applications to energy-momentum tensors in classical field theories and gravity

We prove a theorem on scalar-valued functions of tensors, where ``scalar'' refers to absolute scalars as well as relative scalars of weight $w$. The present work thereby generalizes an identity referred to earlier by Rosenfeld in his publication ``On the energy-momentum tensor''. The theorem provides a $(1,1)$-tensor identity which can be regarded as the tensor analogue of the identity following from Euler's theorem on homogeneous functions. The remarkably simple identity is independent of any internal symmetries of the constituent tensors, providing a powerful tool for deriving relations between field-theoretical expressions and physical quantities. We apply the identity especially for analyzing the metric and canonical energy-momentum tensors of matter and gravity and the relation between them. Moreover, we present a generalized Einstein field equation for arbitrary version of vacuum space-time dynamics -- including torsion and non-metricity. The identity allows to formulate an equivalent representation of this equation. Thereby the conjecture of a zero-energy universe is confirmed.

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arXiv2022

On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation

A modification of the Einstein-Hilbert theory, the Covariant Canonical Gauge Gravity (CCGG), leads to a cosmological constant that represents the energy of the space-time continuum when deformed from its (A)dS ground state to a flat geometry. CCGG is based on the canonical transformation theory in the De Donder-Weyl (DW) Hamiltonian formulation. That framework modifies the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant. The theory predicts a total energy-momentum of the system of space-time and matter to vanish, in line with the conjecture of a "Zero-Energy-Universe" going back to Lorentz (1916) and Levi-Civita (1917). Consequently a flat geometry can only exist in presence of matter where the bulk vacuum energy of matter, regardless of its value, is eliminated by the vacuum energy of space-time.% $\lambda_0$. The observed cosmological constant $\Lambda_{\mathrm{obs}}$ is found to be merely a small correction %of the order $10^{-120} \,\lambda_0$ attributable to deviations from a flat geometry and effects of complex dynamical geometry of space-time, namely torsion and possibly also vacuum fluctuations of matter and space-time. That quadratic extension of General Relativity, anticipated already in 1918 by Einstein \cite{einstein18}, thus provides a significant and natural contribution to resolving the %$120$ orders of magnitude miss-estimate called the "cosmological constant problem".

gr-qc↗

arXiv2019

Canonical transformation path to gauge theories of gravity II --- Spacetime coupling of spin-0 and spin-1 particle fields

The generic form of spacetime dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the Principle of General Relativity. It was thus shown that Einstein's General Relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the "free" (uncoupled) gravitational field, and (ii) the energy-momentum tensor is that of scalar fields representing real or complex structureless (spin-$0$) particles. It followed that all other source fields---such as vector fields representing massive and non-massive spin-$1$ particles---need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and non-massive vector fields. The \emph{massive} vector field has the \emph{canonical} energy-momentum tensor as the appropriate source term---which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of spacetime. In contrast, the system of a \emph{massless} and charged vector field is associated with the \emph{metric} (Hilbert) energy-momentum tensor due to its additional $\mathrm{U}(1)$ symmetry. Moreover, such vector fields do not generate a torsion of spacetime. The respective sources of gravitation apply for all models of the dynamics of the `free' (uncoupled) gravitational field---which do not follow from the gauge formalism but must be specified based on separate physical reasoning.

gr-qc↗

arXiv2018

Pauli-type coupling between spinors and curved spacetime

In this study we prove that the Pauli interaction -- which is associated with a length parameter -- emerges when the minimal coupling recipe is applied to the non-degenerate version of the Dirac Lagrangian. The conventional Dirac Lagrangian is rendered non-degenerate if supplemented by a particular term quadratic in the derivatives of the spinors. For dimensional reasons, this non-degenerate Dirac Lagrangian is associated with a length parameter $\ell$. It yields the standard free Dirac equation in Minkowski space. However, if the Dirac spinor is minimally coupled to gauge fields, then the length parameter~$\ell$ becomes a physical coupling constant yielding novel interactions. For the U($1$) symmetry the Pauli coupling of fermions to electromagnetic fields arises, modifying the fermion's magnetic moment. In a second step we then investigate how analogous "Pauli-type" couplings of gravity and matter arise if fermions are embedded in curved spacetime. Minimal coupling of the Dirac field to the gauge field of gravity, the spin connection, leads to an anomalous spin-torsion interaction and a curvature-dependent mass correction. The relation of the latter to Mach's Principle is discussed. Moreover, it is found for a totally anti-symmetric torsion that an upper limit for the "strength" of the torsion exists in order for a solution to remain causal, while causality for a vector torsion requires a lower limit for its amplitude. We calculate the mass correction in the De~Sitter geometry of vacuum with the cosmological constant $\Lambda$. Possible implications for the existence of effective non-zero rest masses of neutrinos are addressed. Finally, an outlook on the impact of mass correction on the physics of "Big Bang" cosmology, black holes, and of neutron stars is provided.

gr-qc↗

arXiv2018

On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation

A modification of the Einstein-Hilbert theory, the Covariant Canonical Gauge Gravity (CCGG), leads to a cosmological constant that represents the energy of the space-time continuum when deformed from its (A)dS ground state to a flat geometry. CCGG is based on the canonical transformation theory in the De Donder-Weyl (DW) Hamiltonian formulation. That framework modifies the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant. The theory predicts a total energy-momentum of the system of space-time and matter to vanish, in line with the conjecture of a "Zero-Energy-Universe" going back to Lorentz (1916) and Levi-Civita (1917). Consequently a flat geometry can only exist in presence of matter where the bulk vacuum energy of matter, regardless of its value, is eliminated by the vacuum energy of space-time.% $\lambda_0$. The observed cosmological constant $\Lambda_{\mathrm{obs}}$ is found to be merely a small correction %of the order $10^{-120} \,\lambda_0$ attributable to deviations from a flat geometry and effects of complex dynamical geometry of space-time, namely torsion and possibly also vacuum fluctuations. That quadratic extension of General Relativity, anticipated already in 1918 by Einstein \cite{einstein18}, thus provides a significant and natural contribution to resolving the "cosmological constant problem".

gr-qc↗

arXiv2017

Canonical Transformation Path to Gauge Theories of Gravity

In this paper, the generic part of the gauge theory of gravity is derived, based on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the free gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of General Relativity.

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