173 research outputs found
The Fermionic Projector, Entanglement, and the Collapse of the Wave Function
After a brief introduction to the fermionic projector approach, we review how
entanglement and second quantized bosonic and fermionic fields can be described
in this framework. The constructions are discussed with regard to decoherence
phenomena and the measurement problem. We propose a mechanism leading to the
collapse of the wave function in the quantum mechanical measurement process.Comment: 17 pages, LaTeX, 2 figures, minor changes (published version
Non-Existence of Time-Periodic Solutions of the Dirac Equation in a Reissner-Nordstrom Black Hole Background
It is shown analytically that the Dirac equation has no normalizable,
time-periodic solutions in a Reissner-Nordstrom black hole background; in
particular, there are no static solutions of the Dirac equation in such a
background field. The physical interpretation is that Dirac particles can
either disappear into the black hole or escape to infinity, but they cannot
stay on a periodic orbit around the black hole.Comment: 24 pages, 2 figures (published version
The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe
We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and
separate the spatial and time variables. In the case of a closed universe, the
spatial dependence is solved explicitly, giving rise to a discrete set of
solutions. We compute the probability integral and analyze a space-time
normalization integral. This analysis allows us to introduce the fermionic
projector in a closed Friedmann-Robertson-Walker geometry and to specify its
global normalization as well as its local form.Comment: 22 pages, LaTeX, sign error in equation (3.7) correcte
Superconducting Hair on Charged Black String Background
Behaviour of Dirac fermions in the background of a charged black string
penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence
that the system under consideration can support fermion fields acting like a
superconducting cosmic string in the sence that a nontrivial Dirac fermion
field can be carried by the system in question. The case of nonextremal and
extremal black string vortex systems were considered. The influence of electric
and Higgs charge, the winding number and the fermion mass on the fermion
localization near the black string event horizon was studied. It turned out
that the extreme charged black string expelled fermion fields more violently
comparing to the nonextremal one.Comment: RevTex, 16 pages, 12 figures, to be published in Phys.REvD1
The repulsive nature of naked singularities from the point of view of Quantum Mechanics
We use the Dirac equation coupled to a background metric to examine what
happens to quantum mechanical observables like the probability density and the
radial current in the vicinity of a naked singularity of the
Reissner-Nordstr\"{o}m type. We find that the wave function of the Dirac
particle is regular in the point of the singularity. We show that the
probability density is exactly zero at the singularity reflecting
quantum-mechanically the repulsive nature of the naked singularity.
Furthermore, the surface integral of the radial current over a sphere in the
vicinity of the naked singularity turns out to be also zero.Comment: 11 page
Resolvent estimates for normally hyperbolic trapped sets
We give pole free strips and estimates for resolvents of semiclassical
operators which, on the level of the classical flow, have normally hyperbolic
smooth trapped sets of codimension two in phase space. Such trapped sets are
structurally stable and our motivation comes partly from considering the wave
equation for Kerr black holes and their perturbations, whose trapped sets have
precisely this structure. We give applications including local smoothing
effects with epsilon derivative loss for the Schr\"odinger propagator as well
as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5
and Lemma 4.1; this now also corrects hypotheses, explicitly requiring
trapped set to be symplectic. Erratum follows references in this versio
Can Dirac fermions Destroy Yang-Mills Black Hole?
We study the four-dimensional Einstein-Yang-Mills black hole in the presence
of Dirac fermion field. Assuming a spherically symmetric static asymptotically
flat black hole spacetime we consider both massless and massive fermion fields.
The (4+1)-dimensional Einstein-Yang-Mills system effectively reducing to
Einstein-Yang-Mills-Higgs-dilaton model, was also taken into account. One finds
that fermion vacuum leads to the destruction of black holes in question.Comment: 11 pages, RevTEx, to be published in Phys.Rev.D1
A series of coverings of the regular n-gon
We define an infinite series of translation coverings of Veech's double-n-gon
for odd n greater or equal to 5 which share the same Veech group. Additionally
we give an infinite series of translation coverings with constant Veech group
of a regular n-gon for even n greater or equal to 8. These families give rise
to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To
appear in Geometriae Dedicata.
Causal Fermion Systems and Octonions
We compare the structures and methods in the theory of causal fermion systems
with approaches to fundamental physics based on division algebras, in
particular the octonions. We find that octonions and, more generally, tensor
products of division algebras come up naturally to describe the symmetries of
the vacuum configuration of a causal fermion system. This is achieved by
associating the real and imaginary octonion basis elements with the neutrino
and charged sectors of the vacuum fermionic projector, respectively.
Conversely, causal fermion systems provide octonionic theories with spacetime
structures and dynamical equations via the causal action principle. In this
way, octonionic theories and causal fermion systems complement each other.Comment: 36 pages, LaTeX, 1 figur
Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background
We consider the Dirac equation on the background of a Kerr-Newman-de Sitter
black hole. By performing variable separation, we show that there exists no
time-periodic and normalizable solution of the Dirac equation. This conclusion
holds true even in the extremal case. With respect to previously considered
cases, the novelty is represented by the presence, together with a black hole
event horizon, of a cosmological (non degenerate) event horizon, which is at
the root of the possibility to draw a conclusion on the aforementioned topic in
a straightforward way even in the extremal case.Comment: 12 pages. AMS styl
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