6,461 research outputs found
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 second law of thermodynamics, TCP, and Einstein causality in anti-de Sitter space-time
If the vacuum is passive for uniformly accelerated observers in anti-de
Sitter space-time (i.e. cannot be used by them to operate a "perpetuum
mobile"), they will (a) register a universal value of the Hawking-Unruh
temperature, (b) discover a TCP symmetry, and (c) find that observables in
complementary wedge-shaped regions are commensurable (local) in the vacuum
state. These results are model independent and hold in any theory which is
compatible with some weak notion of space-time localization.Comment: 8 pages, slightly improved results, minor changes in the expository
part, new title; to appear in "Classical and Quantum Gravity
The Measurement Process in Local Quantum Theory and the EPR Paradox
We describe in a qualitative way a possible picture of the Measurement
Process in Quantum Mechanics, which takes into account: 1. the finite and non
zero time duration T of the interaction between the observed system and the
microscopic part of the measurement apparatus; 2. the finite space size R of
that apparatus; 3. the fact that the macroscopic part of the measurement
apparatus, having the role of amplifying the effect of that interaction to a
macroscopic scale, is composed by a very large but finite number N of
particles. The conventional picture of the measurement, as an instantaneous
action turning a pure state into a mixture, arises only in the limit in which N
and R tend to infinity, and T tends to 0. We sketch here a proposed scheme,
which still ought to be made mathematically precise in order to analyse its
implications and to test it in specific models, where we argue that in Quantum
Field Theory this picture should apply to the unique time evolution expressing
the dynamics of a given theory, and should comply with the Principle of
Locality. We comment on the Einstein Podolski Rosen thought experiment (partly
modifying the discussion on this point in an earlier version of this note),
reformulated here only in terms of local observables (rather than global ones,
as one particle or polarisation observables). The local picture of the
measurement process helps to make it clear that there is no conflict with the
Principle of Locality.Comment: 18 page
Quantum Field Theory: Where We Are
We comment on the present status, the concepts and their limitations, and the
successes and open problems of the various approaches to a relativistic quantum
theory of elementary particles, with a hindsight to questions concerning
quantum gravity and string theory.Comment: To appear in: An Assessment of Current Paradigms in the Physics of
Fundamental Phenomena, to be published by Springer Verlag (2006
A New Approach to Spin and Statistics
We give an algebraic proof of the spin-statistics connection for the
parabosonic and parafermionic quantum topological charges of a theory of local
observables with a modular PCT-symmetry. The argument avoids the use of the
spinor calculus and also works in 1+2 dimensions. It is expected to be a
progress towards a general spin-statistics theorem including also
(1+2)-dimensional theories with braid group statistics.Comment: LATEX, 15 pages, no figure
On the extension of stringlike localised sectors in 2+1 dimensions
In the framework of algebraic quantum field theory, we study the category
\Delta_BF^A of stringlike localised representations of a net of observables O
\mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)
representations give rise to a non-trivial centre of \Delta_BF^A with respect
to the braiding. This implies that \Delta_BF^A cannot be modular when
non-trival DHR sectors exist. Modular tensor categories, however, are important
for topological quantum computing. For this reason, we discuss a method to
remove this obstruction to modularity.
Indeed, the obstruction can be removed by passing from the observable net
A(O) to the Doplicher-Roberts field net F(O). It is then shown that sectors of
A can be extended to sectors of the field net that commute with the action of
the corresponding symmetry group. Moreover, all such sectors are extensions of
sectors of A. Finally, the category \Delta_BF^F of sectors of F is studied by
investigating the relation with the categorical crossed product of \Delta_BF^A
by the subcategory of DHR representations. Under appropriate conditions, this
completely determines the category \Delta_BF^F.Comment: 36 pages, 1 eps figure; v2: appendix added, minor corrections and
clarification
String-localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with
irreducible representations of the Poincar\'e group and localized in
semi-infinite strings extending to spacelike infinity. Among these are fields
that generate the irreducible representations of mass zero and infinite spin
that are known to be incompatible with point-like localized fields. For the
massive representation and the massless representations of finite helicity, all
string-localized free fields can be written as an integral, along the string,
of point-localized tensor or spinor fields. As a special case we discuss the
string-localized vector fields associated with the point-like electromagnetic
field and their relation to the axial gauge condition in the usual setting.Comment: minor correction
Spectral triples and the super-Virasoro algebra
We construct infinite dimensional spectral triples associated with
representations of the super-Virasoro algebra. In particular the irreducible,
unitary positive energy representation of the Ramond algebra with central
charge c and minimal lowest weight h=c/24 is graded and gives rise to a net of
even theta-summable spectral triples with non-zero Fredholm index. The
irreducible unitary positive energy representations of the Neveu-Schwarz
algebra give rise to nets of even theta-summable generalised spectral triples
where there is no Dirac operator but only a superderivation.Comment: 27 pages; v2: a comment concerning the difficulty in defining cyclic
cocycles in the NS case have been adde
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