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1.
S. L. Woronowicz 《Communications in Mathematical Physics》1972,28(3):221-235
Let
be aC*-algebra and
be an opposite algebra. Notions of exact andj-positive states of
are introduced. It is shown, that any factor state of
can be extended to a pure exactj-positive state
of
. The correspondence
generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states 1 and 2 are quasi-equivalent if and only if their purifications
and
are equivalent. 相似文献
2.
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
3.
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ
2-twisted theories, () and
respectively, which may be constructed from a suitable even Euclidean lattice . Similarly, one may construct lattices
and
by analogous constructions from a doubly-even binary code
. In the case when
is self-dual, the corresponding lattices are also. Similarly, () and
are self-dual if and only if is. We show that
has a natural triality structure, which induces an isomorphism
and also a triality structure on
. For
the Golay code,
is the Leech lattice, and the triality on
is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories () and
with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code. 相似文献
4.
Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal groupSO
e
(5,1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (-sheeted) covering group* of the Minkowskian conformal group SO
e
(4, 2)2. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an -sheeted covering
of Minkowski-spaceM
4. It is known that* can act on this space
and that
admits a globally*-invariant causal ordering;
is thus the natural space on which a globally*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal HamiltonianH=1/2(P
0+K
0).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup
of to unitary representations of*. 相似文献
5.
We study analogues of the Yangian of the Lie algebra
for the other classical Lie algebras
and
. We call them twisted Yangians. They are coideal subalgebras in the Yangian of
and admit homomorphisms onto the universal enveloping algebras U(
) and U(
) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(
) and U(
) of these subalgebras are also maximal commutative. 相似文献
6.
S. L. Woronowicz 《Communications in Mathematical Physics》1973,30(1):55-67
The investigation of purifications of factor states has been carried on. It is shown, that any factor state of aC*-algebra admits at most one purification
, so one can introduce the purification map
. It turns out, that the Powers and Størmer inequality is valid in this general situation. 相似文献
7.
Sergio Doplicher Daniel Kastler Derek W. Robinson 《Communications in Mathematical Physics》1966,3(1):1-28
Starting from aC*-algebra
and a locally compact groupT of automorphisms of
we construct a covariance algebra
with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of
i.e. *-representations of
in which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebra
yielding the *-representations of
in which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of
. Finally we consider the covariance algebra
built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.On leave of absence from Istituto di Fisica G. Marconi — Roma. 相似文献
8.
Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra 总被引:3,自引:0,他引:3
Marc Rosso 《Communications in Mathematical Physics》1988,117(4):581-593
Let
be a complex simple Lie algebra. We show that whent is not a root of 1 all finite dimensional representations of the quantum analogU
t
are completely reducible, and we classify the irreducible ones in terms of highest weights. In particular, they can be seen as deformations of the representations of the (classical)U
. 相似文献
9.
W. Bernreuther G. W. Botz O. Nachtmann P. Overmann 《Zeitschrift fur Physik C Particles and Fields》1991,52(4):567-573
We calculate CP-odd correlations inZ decays to leptons,
. These correlations are sensitive to the weak dipole moment
of the . With 107 producedZ particles and with observation of the decay channels
and v
we estimate that
can be determined with an accuracy of about
(1 s.d.). 相似文献
10.
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat linear operator
, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. Counting lemmas for the non-selfadjoint operator
, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite discD in the complex eigenvalue plane. The radius of the discD is controlled by theH
1 norm of the potential
. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds-whiskered tori for the NLS pde.The Floquet discriminant
is used to introduce a natural sequence of NLS constants of motion, [
, where
c
j
denotes thej
th critical point of the Floquet discriminant ()]. A Taylor series expansion of the constants
, with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of
, which themselves are expressed in terms of quadratic products of eigenfunctions of
. The second variation permits identification, within the disc D, of important bifurcations in the spectral configurations of the operator
. The constant
, as the height of the Floquet discriminant over the critical point
c
j
, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail,
, which is associated with critical points outside the discD. Within this disc, the interpretation is only valid locally, with the same obstruction to its global validity as to a global ordering of the spectrum. Nevertheless, this local Morse theory, together with the Backlund representations of the whiskered tori, produces extremely clear pictures of the stratification of NLS invariant sets near these whiskered tori-pictures which are useful in the study of perturbations of NLS. Finally, a natural connection is noted between the constants
of the integrable theory and Melnikov functions for the theory of perturbations of the NLS equation. This connection generates a simple, but general, representations of the Melnikov functions.Funded in part by AFOSR-90-0161 and by NSF DMS 8922717 A01 相似文献
11.
José M. Figueroa-O'Farrill 《Communications in Mathematical Physics》1996,177(1):129-156
Let
be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if
is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case,
is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra
is equivalent to a vector space decomposition
, where
are isotropic Lie subalgebras. In other words,N=2 structures on
in one-to-one correspondence with Manin triples
. In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures. 相似文献
12.
B. Enriquez 《Communications in Mathematical Physics》1995,170(1):197-206
We propose a quantum lattice version of B. Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of
. We construct an action of the nilpotent part
of
on their lattice counterparts, and embed the lattice variables in a
, coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of
with its dual algebra. 相似文献
13.
A natural supersymmetric extension
is defined of the current (= affine Kac-Moody Lie) algebra
; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of
are constructed. They extend to unitary representations of the semidirect sumS
(G) of
with the superconformal algebra of Neveu-Schwarz, for
, or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria 相似文献
14.
We report numerical data obtained on the special-purpose computer PERCOLA for the exponent
of the electrical conductivity of 2D percolation. The extrapolation yields
and a correction to the scaling exponent=1.2±0.2. 相似文献
15.
An extension of the Supersymmetric Standard Model to the supersymmetricSU(2)
L×SU(2)
R×U(1)
B–L model is considered. The gauge group contains a bidoublet and triplet Higgs field. We investigate the possibility of detecting chargino and neutralino production in
-collisions atCDF, namely
. A numerical analysis is performed for
, tan 1 and a lower bound on the lightest supersymmetric particle (LSP) mass,
GeV. Using conservative assumptions ofM
WR300 GeV andgg
Lg
R, we find the cross sections are:
, and
pb, and thus
L
24
L
at
TeV. Cross sections are also given for larger values of the center of mass energy
up to those available at the SSC. The results are compared with the prompt-lepton background of theW
L, R
–
decays from
. Both decays for
bosons show Jacobian peaks for
(p
T150 GeV forM
WR) at =90°. Furthermore the chargino signature unlike the promptlepton background is symmetric under the Jacobian peak. We also exhibit the dependence of the angular distribution of the chargino on the c.m. angle forp
T40 GeV, 150 GeV at
TeV. 相似文献
16.
We consider the decomposition of the conformal blocks under the conformal embeddings. The case
(â is an affine extension of the abelian subalgebra of the central elements ofgl(lr)) is studied in detal. The reciprocal decompositions of
-modules induce a pairing between the spaces of conformal blocks of
and
Wess-Zumino-Witten models on the Riemann sphere. The completeness of the pairing is shown. Hence it defines aduality between two spaces.Dedicated to Professor Masahisa Adachi on his 60th birthday 相似文献
17.
We formulate the equilibrium correlation functions for local observables of an assembly of non-relativistic, neutral gravitating fermions in the limit where the number of particles becomes infinite, and in a scaling where the region , to which they are confined, remains fixed. We show that these correlation functions correspond, in the limit concerned, to states on the discrete tensor product
, where the
are copies of the gauge invariantC*-algebra
of the CAR overL
2(R
3). The equilibrium states themselves are then given by
, where
, is the Gibbs state on
for an infinitely extended ideal Fermi gas at density , and where 0 is the normalised density function that minimises the Thomas-Fermi functional, obtained in [2], governing the equilibrium thermodynamics of the system. 相似文献
18.
Horng-Tzer Yau 《Communications in Mathematical Physics》1996,181(2):367-408
Let
denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let
be the corresponding canonical measure defined by conditioning
on
. Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed,
is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for
forall chemical potentials . We prove that
for any probability densityf with respect to
; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship. 相似文献
19.
We show that there is a natural gauge invariant presymplectic structure on the spaceA of all vector potentials. The covariant axial anomaly
is found to be the essentially unique infinitestimally equivariant momentum mapping for the action of the group of gauge transformations on (A,). The infinitesimal equivariance of
is shown to be equivalent to the Wess-Zumino consistency condition for the consistent axial anomalyG. We also show that theX operator of Bardeen and Zumino, which relatesG and
, corresponds to the one-form (onA) of the presymplectic structure.Research supported in part by NSF grant MCS 81-08814(A03)Research supported by the U.S. Department of Energy under contract number DE AC02 76 ER 02220 相似文献
20.
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