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1.
Two functionals
and
are introduced forC
*-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals
and
. Our functionals
and
are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya. 相似文献
2.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
3.
Let
be a finite-dimensional complex simple Lie algebra and Uq(
) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of Uq(
), an affinization ofV is an irreducible representationVV of the quantum affine algebra Uq(
) which containsV with multiplicity one and is such that all other irreducible Uq(
)-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of Uq(
) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if
is of typeA, B, C, F orG, the minimal affinization is unique up to Uq(
)-isomorphism; (ii) if
is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of
, there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if Uq(
) is of typeD
4 and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if
is of typeA
n,every affinization is isomorphic to a tensor product of representations of Uq(
) which are irreducible under Uq(
) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701. 相似文献
4.
5.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
6.
We display three equivalent conditions for a sublattice, isomorphic to aP
, of the propositional systemP() of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim
3. We prove that one of them is still necessary and sufficient if dim
<3. A physical interpretation of this condition is given.Wetenschappelijke medewerkers bij het Interuniversitair Instituut voor Kernwetenschappen (in het kader van navorsingsprogramma 21 EN). 相似文献
7.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
8.
J. C. Hurtubise 《Letters in Mathematical Physics》1994,30(2):99-104
We give a classification of the finite dimensional coadjoint orbits in the dual of the algebra
+ of polynomials in one variable with values in a semi-simple Lie algebra
, and generalise this result to algebras defined over an arbitrary Riemann surface.During the preparation of this work the author was supported by NSERC grant A8361 and FCAR grant EQ3518. 相似文献
9.
The property of self-adjointness of the operatorQ =a
+ +a
- in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases when this operator is bounded. Generalized eigenvectors are expressed in terms ofq-Hermite polynomials. If the operatorQ is unbounded, then its closure
is not self-adjoint. However, in this case,
admits self-adjoint extensions. Deficiency subspaces are one-dimensional. These subspaces are explicitly found. 相似文献
10.
A. Bartl W. Majerotto B. Mösslacher N. Oshimo 《Zeitschrift fur Physik C Particles and Fields》1991,52(4):677-684
We present a detailed study of
and
and the subsequent decays of
,
, and
at the LHC
. We explore the relevant supersymmetry parameter range. We calculate the cross sections as well as the rates for interesting signatures such as the production of one or two leptons on the lepton side. 相似文献
11.
We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces
of differential operators transforming p-forms into functions, over
. As an application, we classify the Vect(M)-equivariant maps from
to
over a smooth manifold M, recovering and improving earlier results of N.Poncin. This provides the complete answer to a question raised by P. Lecomte about the extension of a certain intrinsic homotopy operator. 相似文献
12.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
13.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
14.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
15.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献
16.
heide Narnhofer 《Letters in Mathematical Physics》1984,8(6):501-506
For M a factor of type III1 we can find for every automorphism group s that commutes with a modular automorphism group t and another modular automorphism group
, an automorphism group
that commutes with
is connected with s by an inner cocycle. 相似文献
17.
Anatol Odzijewicz 《Letters in Mathematical Physics》1984,8(4):329-335
Starting from conformal kinematics we show that the complex Minkowski space
as a model of time-space is as good as the real one. A holomorphic field theory is constructed on
and it is shown that real field theory is a linear approximation of the holomorphic one. 相似文献
18.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
19.
Given a braided vector space
, we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on
. Using the quantum shuffle construction of the 'upper triangular part'
of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of
. 相似文献
20.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献