3,098 research outputs found
Reduction of Lie-Jordan Banach algebras and quantum states
A theory of reduction of Lie-Jordan Banach algebras with respect to either a
Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared
with the standard reduction of C*-algebras of observables of a quantum system
in the presence of quantum constraints. It is shown that the later corresponds
to the particular instance of the reduction of Lie-Jordan Banach algebras with
respect to a Lie-Jordan subalgebra as described in this paper. The space of
states of the reduced Lie-Jordan Banach algebras is described in terms of
equivalence classes of extensions to the full algebra and their GNS
representations are characterized in the same way. A few simple examples are
discussed that illustrates some of the main results
Coherent states in fermionic Fock-Krein spaces and their amplitudes
We generalize the fermionic coherent states to the case of Fock-Krein spaces,
i.e., Fock spaces with an idefinite inner product of Krein type. This allows
for their application in topological or functorial quantum field theory and
more specifically in general boundary quantum field theory. In this context we
derive a universal formula for the amplitude of a coherent state in linear
field theory on an arbitrary manifold with boundary.Comment: 20 pages, LaTeX + AMS + svmult (included), contribution to the
proceedings of the conference "Coherent States and their Applications: A
Contemporary Panorama" (Marseille, 2016); v2: minor corrections and added
axioms from arXiv:1208.503
Pion-Nucleon Scattering in Kadyshevsky Formalism: I Meson Exchange Sector
In a series of two papers we present the theoretical results of /meson-baryon scattering in the Kadyshevsky formalism. In this paper the
results are given for meson exchange diagrams. On the formal side we show, by
means of an example, how general couplings, i.e. couplings containing multiple
derivatives and/or higher spin fields, should be treated. We do this by
introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For
practical purposes we introduce the method. We also show how the
Takashashi-Umezawa method can be derived using the theory of Bogoliubov and
collaborators and the Gross-Jackiw method is also used to study the
-dependence of the Kadyshevsky integral equation. Last but not least we
present the second quantization procedure of the quasi particle in Kadyshevsky
formalism.Comment: 29 page
Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordstr\"om Black Hole
A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling
Quantum Equivalence Principle for the behaviour of thermal Wightman functions
on an event horizon are analysed in the case of an extremal
Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to
avoid the degeneracy of the metric in the stationary coordinates on the
horizon, a method is introduced which employs the invariant length of geodesics
which pass the horizon. First the method is checked for a massless scalar field
on the event horizon of the Rindler wedge, extending the original procedure of
Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same
results found by Hessling. Afterwards the HNS prescription and Hessling's
prescription for a massless scalar field are analysed on the whole horizon of
an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It
is proved that the weak form of the HNS prescription is satisfyed for all the
finite values of the temperature of the KMS states, i.e., this principle does
not determine any Hawking temperature. It is found that the
Reissner-Nordstr\"{o}m vacuum, i.e., does satisfy the weak HNS
prescription and it is the only state which satisfies weak Hessling's
prescription, too. Finally, it is suggested that all the previously obtained
results should be valid dropping the requirements of a massless field and of a
large mass black hole.Comment: 27 pages, standard LaTex, no figures, final version containing the
results following from Hessling's principle as they appeared in the other
paper gr-qc/9510016, minor changes in the text and in references, it will
appear on Class. Quant. Gra
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
Polymer state approximations of Schroedinger wave functions
It is shown how states of a quantum mechanical particle in the Schroedinger
representation can be approximated by states in the so-called polymer
representation. The result may shed some light on the semiclassical limit of
loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde
A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole
Thermal Wightman functions of a massless scalar field are studied within the
framework of a ``near horizon'' static background model of an extremal R-N
black hole. This model is built up by using global Carter-like coordinates over
an infinite set of Bertotti-Robinson submanifolds glued together. The
analytical extendibility beyond the horizon is imposed as constraints on
(thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It
turns out that only the Bertotti-Robinson vacuum state, i.e. , satisfies
the above requirement. Furthermore the extension of this state onto the whole
manifold is proved to coincide exactly with the vacuum state in the global
Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem
for the Minkowski space-time in terms of Wightman functions holds with
vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum
restricted to a Bertotti-Robinson region, resulting a pure state there, has
vanishing entropy despite of the presence of event horizons. Some comments on
the real extreme R-N black hole are given
Bell inequalities for random fields
The assumptions required for the derivation of Bell inequalities are not
usually satisfied for random fields in which there are any thermal or quantum
fluctuations, in contrast to the general satisfaction of the assumptions for
classical two point particle models. Classical random field models that
explicitly include the effects of quantum fluctuations on measurement are
possible for experiments that violate Bell inequalities.Comment: 18 pages; 1 figure; v4: Essentially the published version; extensive
improvements. v3: Better description of the relationship between classical
random fields and quantum fields; better description of random field models.
More extensive references. v2: Abstract and introduction clarifie
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