Generic Theory of Geometrodynamics from Noether's theorem for the Diff(M) symmetry group

We work out the most general theory for the interaction of spacetime geometry and matter fields---commonly referred to as geometrodynamics---for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i) the action principle should apply and that(ii) the total action should by form-invariant under the (local) diffeomorphism group. The second postulate thus implements the Principle of General Relativity. According to Noether's theorem, this physical symmetry gives rise to a conserved Noether current, from which the complete set of theories compatible with both postulates can be deduced. This finally results in a new generic Einstein-type equation, which can be interpreted as an energy-momentum balance equation emerging from the Lagrangian $L_{R}$ for the source-free dynamics of gravitation and the energy-momentum tensor of the source system $L_{0}$. Provided that the system has no other symmetries---such as SU$(N)$---the canonical energy-momentum tensor turns out to be the correct source term of gravitation. For the case of massive spin particles, this entails an increased weighting of the kinetic energy over the mass in their roles as the source of gravity as compared to the metric energy momentum tensor, which constitutes the source of gravity in Einstein's General Relativity. We furthermore confirm that a massive vector field necessarily acts as a source for torsion of spacetime. Thus, from the viewpoint of our generic Einstein-type equation, Einstein's General Relativity constitutes the particular case for spin-$0$ and massless spin particle fields, and the Hilbert Lagrangian $L_{R,H}$ as the model for the source-free dynamics of gravitation.Comment: 33 page

Dissolution of nucleons in giant nuclei

We discuss the possibility that nuclei with very large baryon numbers can exist in the form of large quark blobs in their ground states. A calculation based on the picture of quark bags shows that, in principle, the appearance of such exotic nuclear states in present laboratory experiments cannot be excluded. Some speculations in connection with the recently observed anomalous positron production in heavy-ion experiments are presented

Covariant Canonical Gauge theory of Gravitation resolves the Cosmological Constant Problem

The covariant canonical transformation theory applied to the relativistic theory of classical matter fields in dynamic space-time yields a new (first order) gauge field theory of gravitation. The emerging field equations embrace a quadratic Riemann curvature term added to Einstein's linear equation. The quadratic term facilitates a momentum field which generates a dynamic response of space-time to its deformations relative to de Sitter geometry, and adds a term proportional to the Planck mass squared to the cosmological constant. The proportionality factor is given by a dimensionless parameter governing the strength of the quadratic term. In consequence, Dark Energy emerges as a balanced mix of three contributions, (A)dS curvature plus the residual vacuum energy of space-time and matter. The Cosmological Constant Problem of the Einstein-Hilbert theory is resolved as the curvature contribution relieves the rigid relation between the cosmological constant and the vacuum energy density of matter

Covariant Canonical Gauge Gravitation and Cosmology

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations necessarily embrace a quadratic Riemann term added to Einstein's linear equation. The quadratic term endows space-time with inertia generating a dynamic response of the space-time geometry to deformations relative to (Anti) de Sitter geometry. A "deformation parameter" is identified, the inverse dimensionless coupling constant governing the relative strength of the quadratic invariant in the Hamiltonian, and directly observable via the deceleration parameter $q_0$. The quadratic invariant makes the system inconsistent with Einstein's constant cosmological term, $\Lambda = \mathrm{const}$. In the Friedman model this inconsistency is resolved with the scaling ansatz of a "cosmological function", $\Lambda(a)$, where $a$ is the scale parameter of the FLRW metric. %Moreover, the strain generated by the quadratic term turns out to act as a geometrical stress. The cosmological function can be normalized such that with the $\Lambda$ CDM parameter set the present-day observables, the Hubble constant and the deceleration parameter, can be reproduced. %We analyze the asymptotics of the such normalized Friedman equations with respect to both, the fundamental parameters (coupling constants) and the scale $a$. With this parameter set we recover the dark energy scenario in the late epoch. The proof that inflation in the early phase is caused by the "geometrical fluid" representing the inertia of space-time is yet pending, though

Canonical Transformation Path to Gauge Theories of Gravity

In this paper, the generic part of the gauge theory of gravity is derived, based merely 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.Comment: 16 page

Covariant Canonical Gauge Theory of Classical Gravitation for Scalar, Vector, and Spin-1/2 Particle Fields

The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor non-metricity are excluded. The manifestly covariant gauge process is based on canonical transformations in the De Donder-Weyl Hamiltonian formalism, starting from a small number of basic postulates. Thereby, the original system of matter fields in flat spacetime, represented by non-degenerate Hamiltonian densities, is amended by spacetime fields. The coupling of matter and spacetime fields leaves the action integral of the combined system invariant under active local Lorentz transformations and passive diffeomorphisms, aka Principle of General Relativity. We consider the Klein-Gordon, Maxwell-Proca, and Dirac fields and derive the corresponding equations of motion. Albeit the coupling of the given matter fields to the gauge fields are unambiguously determined by CCGG, the dynamics of the free gauge fields must be postulated based on physical reasoning. Our choice allows to derive Poisson-like equations of motion also for curvature and torsion. The latter is proven to be totally anti-symmetric. The affine connection is a function of the spin connection and vierbein fields. Requesting the spin connection to be anti-symmetric gives naturally metric compatibility. The canonical equations combine to an extension of the Einstein-Hilbert action with a quadratic Riemann-Cartan concomitant that endows spacetime with inertia. Moreover, a non-degenerate, quadratic version of the free Dirac Lagrangian is deployed. When coupled to gravity, the Dirac equation is endowed with an emergent mass parameter, a curvature-dependent mass correction, and novel interactions between particle spin and spacetime torsion.Comment: Typos removed, formulas added. Will become Chapter 4 in Covariant Canonical Gauge Gravity, to be published by Springer Nature in 202

Collective mechanism of dilepton production in high-energy nuclear collisions

Collective bremsstrahlung of vector meson fields in relativistic nuclear collisions is studied within the time-dependent Walecka model. Mutual deceleration of the colliding nuclei is described by introducing the effective stopping time and average rapidity loss of baryons. It is shown that electromagnetic decays of virtual omega-mesons produced by bremsstrahlung mechanism can provide a substantial contribution to the soft dilepton yield at the SPS bombarding energies. In particular, it may be responsible for the dilepton enhancement observed in 160 AGev central Pb+Au collisions. Suggestions for future experiments to estimate the relative contribution of the collective mechanism are given.Comment: 6 page