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1.
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
2.
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
3.
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
4.
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
5.
The theorem that each derivation of aC*-algebra
extends to an inner derivation of the weak-operator closure (
)– of
in each faithful representation of
is proved in sketch and used to study the automorphism group of
in its norm topology. It is proved that the connected component of the identity in this group contains the open ball of radius 2 with centerl and that each automorphism in extends to an inner automorphism of (
)–.Research conducted with the partial support of the NSF and ONR. 相似文献
6.
Giving an ultraviolet regularization and volume cut off we construct a nuclear Riemannian structure on the Hilbert manifold
of gauge orbits. This permits us to define a regularized Laplace-Beltrami operator on
and an associated global diffusion in
governed by . This enables us to define, via a Feynman-Kac integral, a Euclidean, continuum regularized Yang-Mills process corresponding to a suitable regularization (of the kinetic term) of the classical Yang-Mills Lagrangian onT
.On leave of absence from Zaragoza University (Spain)Laboratoire associé au CNRS 相似文献
7.
Theq=0 combinatorics for
is studied in connection with solvable lattice models. Crystal bases of highest weight representations of
are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of
approximate the crystal graphs of levell representations of
. The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for
.Partially supported by NSF grant MDA904-90-H-4039 相似文献
8.
Using the Godement mean of positive-type functions over a groupG, we study -abelian systems {
, } of aC*-algebra
and a homomorphic mapping of a groupG into the homomorphism group of
. Consideration of the Godement mean off(g)U
g
withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) (
g
(A)) withA
and a covariant representation of the system {
, } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over
. Finally we investigate the discrete spectrum of covariant representations of {
, } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma. 相似文献
9.
Let be a closed * derivation in aC* algebra
which commutes with an ergodic action of a compact group on
. Then generates aC* dynamics of
. Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F. 相似文献
10.
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
11.
Sergio Doplicher Rudolf Haag John E. Roberts 《Communications in Mathematical Physics》1969,15(3):173-200
We wish to study the construction of charge-carrying fields given the representation of the observable algebra in the sector of states of zero charge. It is shown that the set of those covariant sectors which can be obtained from the vacuum sector by acting with localized automorphisms has the structure of a discrete Abelian group. An algebra of fields
can be defined on the Hilbert space of a representation of the observable algebra
which contains each of the above sectors exactly once. The dual group of acts as a gauge group on
in such a way that
is the gauge invariant part of
is made up of Bose and Fermi fields and is determined uniquely by the commutation relations between spacelike separated fields. 相似文献
12.
Representations of theC*-algebra
of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of
onto its commutant. This means that there is an equivalent anti-linear representation of
in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed. 相似文献
13.
It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie groupG with a bi-invariant metric and a generating function suggested in the physics literature, we follow the above line of thought and work out the canonical transformation generated by together with an Ad-invariant metric and a B-field on the associated Lie algebra
ofG so thatG and
form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation including a careful analysis of its domain and image. The geometry of the T-dual structure on
is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper. 相似文献
14.
Sergio Doplicher Rudolf Haag John E. Roberts 《Communications in Mathematical Physics》1969,13(1):1-23
Starting from an algebra of fields
and a compact gauge group of the first kind , the observable algebra
is defined as the gauge invariant part of
. A gauge group of the first kind is shown to be automatically compact if the scattering states are complete and the mass and spin multiplets have finite multiplicity. Under reasonable assumptions about the structure of
it is shown that the inequivalent irreducible representations of
(sectors) which occur are in one-to-one correspondence with the inequivalent irreducible representations of and that all of them are strongly locally equivalent. An irreducible representation of
satisfies the duality property only if the sector corresponds to a 1-dimensional representation of . If is Abelian the sectors are connected to each other by localized automorphisms.On leave of absence from Instituto di Fisica G. Marconi, Università di Roma. 相似文献
15.
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
16.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献
17.
Richard V. Kadison 《Communications in Mathematical Physics》1982,85(1):143-154
Estimates for vector representations of states are used to prove that {C
n
C
0} is strong-operator convergent toC
0, whereC
n is the universal central support of
n
and {
n
} is a sequence of states of aC*-algebra
converging in norm to 0. States of
of a given type are shown to form a norm-closed convex subset of the (norm) dual of
. The pure states of
form a norm-closed subset of the dual.With partial support of the National Science Foundation (USA) 相似文献
18.
Ruedi Suter 《Communications in Mathematical Physics》1994,163(2):359-393
The restricted quantum universal enveloping algebra
decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple
. The indecomposable finite-dimensional
are classified and located in the Auslander-Reiten quiver. 相似文献
19.
G. F. Dell'Antonio 《Communications in Mathematical Physics》1966,2(1):384-397
Given a weakly continuous one-parameter group of automorphisms of aC*-algebra
of operators on a Hilbert space we show that it is implementable by a strongly continuous one-parameter group of unitary operators belonging to the weak closure of
, provided that a certain condition — akin to the boundedness from below of the spectrum of the generators — is satisfied.On leave from the Istituto di Fisica Teorica, Universitá di Napoli. 相似文献
20.
Within the general framework ofC*-algebra approach to mathematical foundation of statistical mechanics, we prove a theorem which gives a natural explanation for the appearance of the chemical potential (as a thermodynamical parameter labelling equilibrium states) in the presence of a symmetry (under gauge transformations of the first kind). As a symmetry, we consider a compact abelian groupG acting as *-automorphisms of aC*-algebra
(quasi-local field algebra) and commuting (elementwise) with the time translation automorphisms
t
of
. Under a technical assumption which is satisfied by examples of physical interest, we prove that the set of all extremal
t
-KMS states (pure phases) ofG-fixed-point subalgebra
(quasi-local observable algebra) of
satisfying a certain faithfulness condition is in one-to-one correspondence with the set of all extremalG-invariant
t
·
t
-KMS states – of
with varying over one-parameter subgroups ofG (the specification of being the specification of the chemical potential), where the correspondence is that the restriction of – to
is . 相似文献