304 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
Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
We consider a spatially homogeneous and isotropic system of Dirac particles
coupled to classical gravity. The dust and radiation dominated closed
Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find
a mechanism where quantum oscillations of the Dirac wave functions can prevent
the formation of the big bang or big crunch singularity. Thus before the big
crunch, the collapse of the universe is stopped by quantum effects and reversed
to an expansion, so that the universe opens up entering a new era of classical
behavior.
Numerical examples of such space-times are given, and the dependence on
various parameters is discussed. Generically, one has a collapse after a finite
number of cycles. By fine-tuning the parameters we construct an example of a
space-time which is time-periodic, thus running through an infinite number of
contraction and expansion cycles.Comment: 8 pages, LaTeX, 4 figures, statement on energy conditions correcte
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
Formation of methylmercaptan and dimethylsulfide from methoxylated aromatic compounds in anoxic marine and fresh water sediments
Anaerobic formation of dimethylsulfide (DMS) and methylmercaptan (MSH) in anoxic sulfide-containing slurries from marine and fresh water sediments was stimulated by addition of syringate (4-hydroxy,3,5,-dimethoxybenzoate) and 3,4,5,-trimethoxybenzoate. The release of DMS and MSH occurred during the consumption of the aromatic monomers and ceased after their depletion. DMS was the dominant methylated sulfur compound in fresh water sediments, in contrast to marine sediments where MSH was predominant. No production of volatile organic sulfur compounds was observed in slurries containing gallate (3,4,5,-trihydroxybenzoate) or in autoclaved controled. About 50-65% of the methoxy carbon could be accounted for by peak accumulation of DMS and MSH. In the saline sediments, large amounts of CH4 were formed during the period when DMS and MSH disappeared. About 65-70% of the methylcarbon of the volatile methylated sulfur compounds (VMSC) could be accounted for in the produced CH4. This study demonstrates a previously unknown microbial process by which DMS and MSH are formed during anaerobic decomposition of methoxylated aromatic compounds in marine and freshwater sediments. © 1990
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
Causal Fermion Systems and the ETH Approach to Quantum Theory
After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length
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
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
A mechanism for dark matter and dark energy in the theory of causal fermion systems
It is shown that the theory of causal fermion systems gives rise to a novel mechanism for dark matter and dark energy. This mechanism is first worked out for cubical subsets of Minkowski space with periodic boundary conditions. Then it is studied in Friedmann–Lemaître–Roberson–Walker spacetimes. The magnitude of the effect scales like one over the lifetime of the Universe squared. In contrast to most models of dark matter and dark energy, our mechanism does not postulate any new particles. Instead, it is a result of the collective behavior of all the wave functions which form the Dirac sea, needed in order to arrange correlated initial and end quantum states of the Universe
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