101 research outputs found
Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
A noncommutative geometric generalisation of the quantum field theoretical
framework is developed by generalising the Heisenberg commutation relations.
There appear nonzero minimal uncertainties in positions and in momenta. As the
main result it is shown with the example of a quadratically ultraviolet
divergent graph in theory that nonzero minimal uncertainties in
positions do have the power to regularise. These studies are motivated with the
ansatz that nonzero minimal uncertainties in positions and in momenta arise
from gravity. Algebraic techniques are used that have been developed in the
field of quantum groups.Comment: 52 pages LATEX, DAMTP/93-33. Revised version now includes a chapter
on the Poincare algebra and curvature as noncommutativity of momentum spac
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
Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom
Based only on classical Hamiltonian dynamics, we prove the maximum work
principle in a system where macroscopic dynamical degrees of freedom are
intrinsically coupled to microscopic degrees of freedom. Unlike recent
identities between irreversible work and free energy, such as in the Jarzynski
relation, the macroscopic dynamics is not governed by an external action but
undergoes the back reaction of the microscopic degrees of freedom. Our theorems
cover such physical situations as impact between macroscopic bodies,
thermodynamic machines, and molecular motors.Comment: 4 pages, RevTe
Kakutani Dichotomy on Free States
Two quasi-free states on a CAR or CCR algebra are shown to generate
quasi-equivalent representations unless they are disjoint.Comment: 12 page
Unbounded representations of -deformation of Cuntz algebra
We study a deformation of the Cuntz-Toeplitz -algebra determined by the
relations . We define well-behaved unbounded
*-representations of the *-algebra defined by relations above and classify all
such irreducible representations up to unitary equivalence.Comment: 13 pages, Submitted to Lett. Math. Phy
Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
Covariant differential calculi and exterior algebras on quantum homogeneous
spaces endowed with the action of inhomogeneous quantum groups are classified.
In the case of quantum Minkowski spaces they have the same dimensions as in the
classical case. Formal solutions of the corresponding Klein--Gordon and Dirac
equations are found. The Fock space construction is sketched.Comment: 21 pages, LaTeX file, minor change
Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras
We formulate a theory of generalized Fock spaces which underlies the
different forms of quantum statistics such as ``infinite'', Bose-Einstein and
Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems
that cannot be mapped into single-indexed systems are studied. Our theory is
based on a three-tiered structure consisting of Fock space, statistics and
algebra. This general formalism not only unifies the various forms of
statistics and algebras, but also allows us to construct many new forms of
quantum statistics as well as many algebras of creation and destruction
operators. Some of these are : new algebras for infinite statistics,
q-statistics and its many avatars, a consistent algebra for fractional
statistics, null statistics or statistics of frozen order, ``doubly-infinite''
statistics, many representations of orthostatistics, Hubbard statistics and its
variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43.
Published versio
The H\"older Inequality for KMS States
We prove a H\"older inequality for KMS States, which generalises a well-known
trace-inequality. Our results are based on the theory of non-commutative
-spaces.Comment: 10 page
Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
We analyze the hamiltonian quantization of Chern-Simons theory associated to
the universal covering of the Lorentz group SO(3,1). The algebra of observables
is generated by finite dimensional spin networks drawn on a punctured
topological surface. Our main result is a construction of a unitary
representation of this algebra. For this purpose, we use the formalism of
combinatorial quantization of Chern-Simons theory, i.e we quantize the algebra
of polynomial functions on the space of flat SL(2,C)-connections on a
topological surface with punctures. This algebra admits a unitary
representation acting on an Hilbert space which consists in wave packets of
spin-networks associated to principal unitary representations of the quantum
Lorentz group. This representation is constructed using only Clebsch-Gordan
decomposition of a tensor product of a finite dimensional representation with a
principal unitary representation. The proof of unitarity of this representation
is non trivial and is a consequence of properties of intertwiners which are
studied in depth. We analyze the relationship between the insertion of a
puncture colored with a principal representation and the presence of a
world-line of a massive spinning particle in de Sitter space.Comment: 78 pages. Packages include
Some remarks on the Gauss decomposition for quantum group GL_q(n)
In this letter some properties of the Gauss decomposition of quantum group
with application to q-bosonization are considered.Comment: 11 page
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