721 research outputs found
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- and
spin- 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 for the source-free dynamics of gravitation and the
energy-momentum tensor of the source system . Provided that the system
has no other symmetries---such as SU---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- and massless spin particle fields,
and the Hilbert Lagrangian 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 . The quadratic invariant makes the system
inconsistent with Einstein's constant cosmological term, . In the Friedman model this inconsistency is resolved with the
scaling ansatz of a "cosmological function", , where 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 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 . 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
- …