140 research outputs found
Remarks on matter-gravity entanglement, entropy, information loss and events
I recall my 'matter-gravity entanglement hypothesis' and briefly review the
evidence for it, based partly on its seeming ability to resolve a number of
puzzles related to quantum black holes including the black hole information
loss puzzle. I point out that, according to this hypothesis, there is a
quantity, i.e. the universe's 'matter-gravity entanglement entropy' -- which
deserves to be considered the 'entropy of the universe' and which, with
suitable initial conditions, will plausibly increase monotonically with
cosmological time. In the last section, which is more tentative and raises a
number of further puzzles and open questions, I discuss the prospects for a
notion of 'events' which 'happen' whose statistical properties are described by
this entropy of the universe. It is hoped that such a theory of events may be a
step on the way towards explaining how initial quantum fluctuations convert
themselves into inhomogeneities in a seemingly classical universe.Comment: 17 pages, 7 figures. Invited contribution to the proceedings of the
conference "Progress and Visions in Quantum Theory in View of Gravity",
Leipzig, Germany, October 2018, based on part of a talk at the workshop "The
Mysterious Universe: Dark Matter -- Dark Energy -- Cosmic Magnetic Fields"
MITP, Mainz, Germany, June 4, 2019. (v2 No change) v3: References added v4:
typos etc. correcte
Exact factorization of the time-dependent electron-nuclear wavefunction
We present an exact decomposition of the complete wavefunction for a system
of nuclei and electrons evolving in a time-dependent external potential. We
derive formally exact equations for the nuclear and electronic wavefunctions
that lead to rigorous definitions of a time-dependent potential energy surface
(TDPES) and a time-dependent geometric phase. For the molecular ion
exposed to a laser field, the TDPES proves to be a useful interpretive tool to
identify different mechanisms of dissociation.Comment: 4 pages, 2 figure
Quantized reduction as a tensor product
Symplectic reduction is reinterpreted as the composition of arrows in the
category of integrable Poisson manifolds, whose arrows are isomorphism classes
of dual pairs, with symplectic groupoids as units. Morita equivalence of
Poisson manifolds amounts to isomorphism of objects in this category.
This description paves the way for the quantization of the classical
reduction procedure, which is based on the formal analogy between dual pairs of
Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with
correspondences between von Neumann algebras. Further analogies are drawn with
categories of groupoids (of algebraic, measured, Lie, and symplectic type). In
all cases, the arrows are isomorphism classes of appropriate bimodules, and
their composition may be seen as a tensor product. Hence in suitable categories
reduction is simply composition of arrows, and Morita equivalence is
isomorphism of objects.Comment: 44 pages, categorical interpretation adde
Consistent quantum mechanics admits no mereotopology
It is standardly assumed in discussions of quantum theory that physical
systems can be regarded as having well-defined Hilbert spaces. It is shown here
that a Hilbert space can be consistently partitioned only if its components are
assumed not to interact. The assumption that physical systems have well-defined
Hilbert spaces is, therefore, physically unwarranted.Comment: 10 pages; to appear in Axiomathe
Some Field Theoretic Issues Regarding the Chiral Magnetic Effect
In this paper, we shall address some field theoretic issues regarding the
chiral magnetic effect. The general structure of the magnetic current
consistent with the electromagnetic gauge invariance is obtained and the impact
of the infrared divergence is examined. Some subtleties on the relation between
the chiral magnetic effect and the axial anomaly are clarified through a
careful examination of the infrared limit of the relevant thermal diagrams.Comment: 19 pages, 4 figures in Latex. Typos fixed, version accepted to be
published in JHE
Holographic Anomalous Conductivities and the Chiral Magnetic Effect
We calculate anomaly induced conductivities from a holographic gauge theory
model using Kubo formulas, making a clear conceptual distinction between
thermodynamic state variables such as chemical potentials and external
background fields. This allows us to pinpoint ambiguities in previous
holographic calculations of the chiral magnetic conductivity. We also calculate
the corresponding anomalous current three-point functions in special kinematic
regimes. We compare the holographic results to weak coupling calculations using
both dimensional regularization and cutoff regularization. In order to
reproduce the weak coupling results it is necessary to allow for singular
holographic gauge field configurations when a chiral chemical potential is
introduced for a chiral charge defined through a gauge invariant but
non-conserved chiral density. We argue that this is appropriate for actually
addressing charge separation due to the chiral magnetic effect.Comment: 17 pages, 1 figure. v2: 18 pages, 1 figure, discussion clarified
throughout the text, references added, version accepted for publication in
JHE
Notions of Infinity in Quantum Physics
In this article we will review some notions of infiniteness that appear in
Hilbert space operators and operator algebras. These include proper
infiniteness, Murray von Neumann's classification into type I and type III
factors and the class of F{/o} lner C*-algebras that capture some aspects of
amenability. We will also mention how these notions reappear in the description
of certain mathematical aspects of quantum mechanics, quantum field theory and
the theory of superselection sectors. We also show that the algebra of the
canonical anti-commutation relations (CAR-algebra) is in the class of F{/o}
lner C*-algebras.Comment: 11 page
Coherent states for compact Lie groups and their large-N limits
The first two parts of this article surveys results related to the
heat-kernel coherent states for a compact Lie group K. I begin by reviewing the
definition of the coherent states, their resolution of the identity, and the
associated Segal-Bargmann transform. I then describe related results including
connections to geometric quantization and (1+1)-dimensional Yang--Mills theory,
the associated coherent states on spheres, and applications to quantum gravity.
The third part of this article summarizes recent work of mine with Driver and
Kemp on the large-N limit of the Segal--Bargmann transform for the unitary
group U(N). A key result is the identification of the leading-order large-N
behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states
and their applications: A contemporary panorama.
Quantum Field Theoretic Description of Matter in the Universe
Quantum field theory at finite temperature and density can be used for
describing the physics of relativistic plasmas. Such systems are frequently
encountered in astrophysical situations, such as the early Universe, Supernova
explosions, and the interior of neutron stars. After a brief introduction to
thermal field theory the usefulness of this approach in astrophysics will be
exemplified in three different cases. First the interaction of neutrinos within
a Supernova plasma will be discussed. Then the possible presence of quark
matter in a neutron star core and finally the interaction of light with the
Cosmic Microwave Background will be considered.Comment: 7 pages, 9 figures, to be published in the Proceedings of the ISSI
Workshop "Matter in the Universe" (Bern, March 19-23, 2001), misprints
correcte
Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization
For arbitrary compact quantizable Kähler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential manner. It is shown that the star product is null on constants and fulfills parity. A trace is constructed and the relation to deformation quantization by geometric quantization is given
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