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László B Szabados

Publications and source records attributed to László B Szabados.

9 recordsLinked to original sources
arXiv2023

The 'most classical' states of Euclidean invariant elementary quantum mechanical systems

Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of Euclidean invariant elementary quantum mechanical systems, even with non-zero intrinsic spin. It is shown that while there is a 1-parameter family of such states for any two components of the angular momentum vector operator with any angle between them, such states exist for a component of the linear and angular momenta \emph{only if} these components are orthogonal to each other and hence the problem is reduced to the two-dimensional Euclidean invariant case. We also show that the analogous states exist for a component of the linear momentum and of the centre-of-mass vector \emph{only if} the angle between them is zero or an acute angle. \emph{No} such state (represented by a square integrable and differentiable wave function) can exist for \emph{any} pair of components of the centre-of-mass vector operator. Therefore, the existence of such states depends not only on the Lie algebra, but on the choice for its generators as well.

quant-ph↗
arXiv2018

Gravity, as a classical regulator for the Higgs field, and the origin of rest masses and electric charge

The classical Einstein--Standard Model system with conformally invariant coupling of the Higgs field to gravity is investigated. We show that the energy-momentum tensor is not polynomial in the Higgs field, and hence it may have two singularities: In cosmological spacetimes the usual Big Bang type singularity with diverging matter field variables, and a second, less violent one (Small Bang), in which it is only the geometry that is singular but the matter field variables remain finite. In generic spacetimes, the latter provides a finite, universal upper bound for the pointwise norm of the Higgs field in terms of Newton's gravitational constant. We also show that, in the presence of Friedman--Robertson--Walker or Kantowski--Sachs symmetries, the energy density can have finite local minimum only if the transitivity hypersurfaces of the spacetime symmetries are locally hyperboloidal and their mean curvature is less than a finite critical value. In particular, in the very early era of an expanding universe or in a nearly spherically symmetric black hole near the central singularity, the Higgs sector does not have any instantaneous vacuum state, and hence its rest mass is not defined, and, via the Brout--Englert--Higgs (BEH) mechanism, the gauge and spinor fields do not get non-zero rest mass. For smaller mean curvature instantaneous symmetry breaking vacuum states of the Higgs sector emerge, yielding non-zero rest mass and electric charge for some of the gauge and spinor fields via the BEH mechanism. These rest masses are decreasing with decreasing mean curvature, but the charge remains constant. It is also shown that globally defined instantaneous vacuum states that are invariant with respect to the spacetime symmetries do not exist at all in the $k=1,0$ cosmological models and in Kantowski--Sachs spacetimes (e.g. inside spherically symmetric black holes).

gr-qc↗
arXiv2017

The evanescence of rest masses and electric charge in black holes

The classical Einstein-Standard Model system with conformally invariant coupling of the Higgs field to gravity is investigated in nearly Schwarzschild black holes. We show that, in the presence of Kantowski-Sachs symmetries, there is a finite critical value of the mean curvature such that on spacelike hypersurfaces with greater mean curvature the Higgs sector does not have any symmetry breaking vacuum state. Hence, according to the Standard Model of particle physics, the gauge and spinor fields do not have rest mass and electric charge. Therefore, particles falling into a nearly Schwarzschild black hole lose their mass and charge in the "reverse" Brout-Englert-Higgs mechanism.

gr-qc↗
arXiv2015

A positive Bondi--type mass in asymptotically de Sitter spacetimes

The general structure of the conformal boundary $\mathscr{I}^+$ of asymptotically de Sitter spacetimes is investigated. First we show that Penrose's quasi-local mass, associated with a cut ${\cal S}$ of the conformal boundary, can be zero even in the presence of outgoing gravitational radiation. On the other hand, following a Witten--type spinorial proof, we show that an analogous expression based on the Nester--Witten form is finite only if the Witten spinor field solves the 2-surface twistor equation on ${\cal S}$, and it yields a positive functional on the 2-surface twistor space on ${\cal S}$, provided the matter fields satisfy the dominant energy condition. Moreover, this functional is vanishing if and only if the domain of dependence of the spacelike hypersurface which intersects $\mathscr{I}^+$ in the cut ${\cal S}$ is locally isometric to the de Sitter spacetime. For non-contorted cuts this functional yields an invariant analogous to the Bondi mass.

gr-qc↗
arXiv2013

On the total mass of closed universes

The total mass, the Witten type gauge conditions and the spectral properties of the Sen-Witten and the 3-surface twistor operators in closed universes are investigated. It has been proven that a recently suggested expression ${\tt M}$ for the total mass density of closed universes is vanishing if and only if the spacetime is flat with toroidal spatial topology; it coincides with the first eigenvalue of the Sen-Witten operator; and it is vanishing if and only if Witten's gauge condition admits a non-trivial solution. Here we generalize slightly the result above on the zero-mass configurations: ${\tt M}=0$ if and only if the spacetime is holonomically trivial with toroidal spatial topology. Also, we show that the multiplicity of the eigenvalues of the (square of the) Sen-Witten operator is at least two, and a potentially viable gauge condition is suggested. The monotonicity properties of ${\tt M}$ through the examples of closed Bianchi I and IX cosmological spacetimes are also discussed. A potential spectral characterization of these cosmological spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the Sen-Witten and the 3-surface twistor operators, is also indicated.

gr-qc↗
arXiv2013

On the total mass of closed universes with a positive cosmological constant

The recently suggested notion of total mass density for closed universes is extended to closed universes with a positive cosmological constant. Assuming that the matter fields satisfy the dominant energy condition, it is shown that the cosmological constant provides a sharp lower bound for the total mass density, and that the total mass density takes this as its minimum value if and only if the spacetime is locally isometric with the de Sitter spacetime. This notion of total mass density is extensible to non-compact three-spaces of homogeneity of Bianchi class A cosmological spacetimes.

gr-qc↗
arXiv2012

A note on the post-Newtonian limit of quasi-local energy expressions

An `effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact GR as the volume integral of all the source terms in the field equation for the Newtonian potential in static spacetimes. In particular, we exhibit a new post-Newtonian correction in the source term in the field equation for the Newtonian gravitational potential. In asymptotically flat spacetimes this expression tends to the ADM energy at the spatial infinity as a {\em monotonically decreasing} set function. We prove its positivity in spherically symmetric spacetimes under certain energy conditions, and that its vanishing characterizes flatness. We argue that any physically acceptable quasi-local energy expression should behave qualitatively like this `effective' energy expression in this limit.

gr-qc↗
arXiv2011

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.

gr-qc↗