58 research outputs found
Lightfront holography and area density of entropy associated with localization on wedge-horizons
It is shown that a suitably formulated algebraic lightfront holography, in
which the lightfront is viewed as the linear extension of the upper causal
horizon of a wedge region, is capable of overcoming the shortcomings of the old
lightfront quantization. The absence of transverse vacuum fluctuations which
this formalism reveals, is responsible for an area (edge of the wedge)
-rearrangement of degrees of freedom which in turn leads to the notion of area
density of entropy for a ``split localization''. This area proportionality of
horizon associated entropy has to be compared to the volume dependence of
ordinary heat bath entropy. The desired limit, in which the split distance
vanishes and the localization on the horizon becomes sharp, can at most yield a
relative area density which measures the ratio of area densities for different
quantum matter. In order to obtain a normalized area density one needs the
unknown analog of a second fundamental law of thermodynamics for thermalization
caused by vacuum fluctuation through localization on causal horizons. This is
similar to the role of the classical Gibbs form of that law which relates
Bekenstein's classical area formula with the Hawking quantum mechanism for
thermalization from black holes. PACS: 11.10.-z, 11.30.-j, 11.55.-mComment: The last two sections have been modified. This is the form in which
the paper will be published in IJP
Charged sectors, spin and statistics in quantum field theory on curved spacetimes
The first part of this paper extends the Doplicher-Haag-Roberts theory of
superselection sectors to quantum field theory on arbitrary globally hyperbolic
spacetimes. The statistics of a superselection sector may be defined as in flat
spacetime and each charge has a conjugate charge when the spacetime possesses
non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes
with appropriate symmetries. Two situations are considered: First, if the
spacetime has a bifurcate Killing horizon, as is the case in the presence of
black holes, then restricting the observables to the Killing horizon together
with "modular covariance" for the Killing flow yields a conformally covariant
quantum field theory on the circle and a conformal spin-statistics theorem for
charged sectors localizable on the Killing horizon. Secondly, if the spacetime
has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes,
"geometric modular action" of the rotational symmetry leads to a
spin-statistics theorem for charged covariant sectors where the spin is defined
via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page
Endomorphism Semigroups and Lightlike Translations
Certain criteria are demonstrated for a spatial derivation of a von Neumann
algebra to generate a one-parameter semigroup of endomorphisms of that algebra.
These are then used to establish a converse to recent results of Borchers and
of Wiesbrock on certain one-parameter semigroups of endomorphisms of von
Neumann algebras (specifically, Type III_1 factors) that appear as lightlike
translations in the theory of algebras of local observables.Comment: 9 pages, Late
Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II
In the first part, we have constructed several families of interacting
wedge-local nets of von Neumann algebras. In particular, there has been
discovered a family of models based on the endomorphisms of the U(1)-current
algebra of Longo-Witten.
In this second part, we further investigate endomorphisms and interacting
models. The key ingredient is the free massless fermionic net, which contains
the U(1)-current net as the fixed point subnet with respect to the U(1) gauge
action. Through the restriction to the subnet, we construct a new family of
Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting
wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the
structure of particle numbers and the S-matrices of the models constructed here
do mix the spaces with different particle numbers of the bosonic Fock space.Comment: 33 pages, 1 tikz figure. The final version is available under Open
Access. CC-B
There are No Causality Problems for Fermi's Two Atom System
A repeatedly discussed gedanken experiment, proposed by Fermi to check
Einstein causality, is reconsidered. It is shown that, contrary to a recent
statement made by Hegerfeldt, there appears no causality paradoxon in a proper
theoretical description of the experiment.Comment: 6 pages, latex, DESY 94-02
The averaged null energy condition for general quantum field theories in two dimensions
It is shown that the averaged null energy condition is fulfilled for a dense,
translationally invariant set of vector states in any local quantum field
theory in two-dimensional Minkowski spacetime whenever the theory has a mass
gap and possesses an energy-momentum tensor. The latter is assumed to be a
Wightman field which is local relative to the observables, generates locally
the translations, is divergence-free, and energetically bounded. Thus the
averaged null energy condition can be deduced from completely generic, standard
assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
We present a method of short-distance analysis in quantum field theory that
does not require choosing a renormalization prescription a priori. We set out
from a local net of algebras with associated pointlike quantum fields. The net
has a naturally defined scaling limit in the sense of Buchholz and Verch; we
investigate the effect of this limit on the pointlike fields. Both for the
fields and their operator product expansions, a well-defined limit procedure
can be established. This can always be interpreted in the usual sense of
multiplicative renormalization, where the renormalization factors are
determined by our analysis. We also consider the limits of symmetry actions. In
particular, for suitable limit states, the group of scaling transformations
induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
The Quest for Understanding in Relativistic Quantum Physics
We discuss the status and some perspectives of relativistic quantum physics.Comment: Invited contribution to the Special Issue 2000 of the Journal of
Mathematical Physics, 38 pages, typos corrected and references added, as to
appear in JM
The paradigm of the area law and the structure of transversal and longitudinal lightfront degrees of freedom
It is shown that an algebraically defined holographic projection of a QFT
onto the lightfront changes the local quantum properties in a very drastic way.
The expected ubiquitous vacuum polarization characteristic of QFT is confined
to the lightray (longitudinal) direction, whereas operators whose localization
is transversely separated are completely free of vacuum correlations. This
unexpected ''transverse return to QM'' combined with the rather universal
nature of the strongly longitudinal correlated vacuum correlations (which turn
out to be described by rather kinematical chiral theories) leads to a d-2
dimensional area structure of the d-1 dimensional lightfront theory. An
additive transcription in terms of an appropriately defined entropy related to
the vacuum restricted to the horizon is proposed and its model independent
universality aspects which permit its interpretation as a quantum candidate for
Bekenstein's area law are discussed. The transverse tensor product foliation
structure of lightfront degrees of freedom is essential for the simplifying
aspects of the algebraic lightcone holography. Key-words: Quantum field theory;
Mathematical physics, Quantum gravityComment: 16 pages latex, identical to version published in JPA: Math. Gen. 35
(2002) 9165-918
Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy
It is shown that certain kinds of behavior, which hitherto were expected to
be characteristic for classical gravity and quantum field theory in curved
spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography
on event horizons and an area proportionality of entropy, have in fact an
unnoticed presence in Minkowski QFT. This casts new light on the fundamental
question whether the volume propotionality of heat bath entropy and the
(logarithmically corrected) dimensionless area law obeyed by
localization-induced thermal behavior are different geometric parametrizations
which share a common primordeal algebraic origin. Strong arguments are
presented that these two different thermal manifestations can be directly
related, this is in fact the main aim of this paper. It will be demonstrated
that QFT beyond the Lagrangian quantization setting receives crucial new
impulses from holography onto horizons. The present paper is part of a project
aimed at elucidating the enormous physical range of "modular localization". The
latter does not only extend from standard Hamitonian heat bath thermal states
to thermal aspects of causal- or event- horizons addressed in this paper. It
also includes the recent understanding of the crossing property of formfactors
whose intriguing similarity with thermal properties was, although sometimes
noticed, only sufficiently understood in the modular llocalization setting.Comment: 42 pages, changes, addition of new results and new references, in
this form the paper will appear in Foundations of Physic
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