130 research outputs found
Functional form of unitary representations of the quantum "az+b" group
The formula for all unitary representations of the quantum "az+b" group for a
real deformation parameter is given. The description involves the quantum
exponential function introduced by Woronowicz
Extensions of Lieb's concavity theorem
The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded
self-adjoint operators in the domain of a function f of two real variables, is
convex for every Hilbert Schmidt operator K, if and only if f is operator
convex. As a special case we obtain a new proof of Lieb's concavity theorem for
the function (A,B)\to\tr A^pK^*B^{q}K, where p and q are non-negative numbers
with sum p+q\le 1. In addition, we prove concavity of the operator function
(A,B)\to \tr(A(A+\mu_1)^{-1}K^* B(B+\mu_2)^{-1}K) on its natural domain
D_2(\mu_1,\mu_2), cf. Definition 4.1Comment: The format of one reference is changed such that CiteBase can
identify i
Cartan Pairs
A new notion of Cartan pairs as a substitute of notion of vector fields in
noncommutative geometry is proposed. The correspondence between Cartan pairs
and differential calculi is established.Comment: 7 pages in LaTeX, to be published in Czechoslovak Journal of Physics,
presented at the 5th Colloquium on Quantum Groups and Integrable Systems,
Prague, June 199
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
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
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
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
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
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