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1.
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
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.
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
4.
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
5.
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators
. The reduction of the Poisson structure to the symplectic submanifold
gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as
, where
means the multiplicity of roots and to the case (b) is defined by
where
is the multiplicity of poles. We prove that
-algebra is isomorphic via a transformation to
U(1) with m=
. We also give the explicit free fields representations for these W-algebras. 相似文献
6.
The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 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.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
9.
For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators
for some self-adjoint operator
and some *-representation of the underlying *-algebra. 相似文献
10.
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
11.
We show that there are canonical isomorphisms between Hochschild cohomology spaces
, where
is the algebra of smooth functions on a manifold M and
the space of skew multivector fields over M. This implies that continuous and differential deformation theories of
coincide. 相似文献
12.
We briefly report on new results concerning a perturbation expansion structure within the framework of an analytic version of perturbative quantum chromodynamics (pQCD). This approach combines the RG symmetry with the Källén–Lehmann analyticity in the Q2 variable. The procedure of analytization matches this analyticity with the RG invariance by adding to the analytized invariant coupling
some nonperturbative contributions containing no adjustable parameters. In turn, the new perturbative expansion (the APT expansion) for an observable represents asymptotic expansion over a nonpower set of specific functions
rather than in powers of
. We analyze this set and show that it obeys different properties in various ranges of the Q2 variable. In the UV, it is close to the power set
used in the pQCD calculation. However, generally, this set is of a more complicated nature. In the low Q2 region the behavior of
is oscillating. Here, the APT expansion has a feature of asymptotic expansion à la Erdélyi. The issue of the consistency of an analytization procedure with the RG structure of observables is also discussed. 相似文献
13.
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
14.
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
15.
Motivated by deformation quantization, we consider in this paper *-algebras
over rings
=
(i), where
is an ordered ring and I2=–1, and study the deformation theory of projective modules over these algebras carrying the additional structure of a (positive)
-valued inner product. For A=C
(M), M a manifold, these modules can be identified with Hermitian vector bundles E over M. We show that for a fixed Hermitian star product on M, these modules can always be deformed in a unique way, up to (isometric) equivalence. We observe that there is a natural bijection between the sets of equivalence classes of local Hermitian deformations of C
(M) and (
(E)) and that the corresponding deformed algebras are formally Morita equivalent, an algebraic generalization of strong Morita equivalence of C
*-algebras. We also discuss the semi-classical geometry arising from these deformations. 相似文献
16.
Lu has shown that any dynamical r-matrix for the pair (
,
) naturally induces a Poisson homogeneous structure on G/U. She also proved that if
is complex simple,
is its Cartan subalgebra and r is quasitriangular, then this correspondence is in fact one-to-one. In this Letter we find some general conditions under which the Lu correspondence is one-to-one. Then we apply this result to describe all triangular Poisson homogeneous structures on G/U for a simple complex group G and its reductive subgroup U containing a Cartan subgroup. 相似文献
17.
Let A, B be positive operators on a Hilbert space, z any complex number, m any positive integer, and
any unitarily invariant norm. We show that
and
Some related inequalities are also obtained. 相似文献
18.
We construct embeddings of boundary algebras
into ZF algebras
. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for
and without for
), this connection allows to make the link between different approaches of the systems with boundaries. The construction uses the well-bred vertex operators built recently, and is classified by reflection matrices. It relies only on the existence of an R-matrix obeying a unitarity condition, and as such can be applied to any infinite dimensional quantum group. 相似文献
19.
Given n2, we put r=min
. Let be a compact, C
r
-smooth surface in n which contains the origin. Let further
be a family of measurable subsets of such that
as
. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator
in L
2(
n
), where is a positive constant, as
. An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve. 相似文献
20.
We study all possible U(1)-extensions of the standard model within the framework of noncommutative geometry with the algebra
. Comparison to experimental data about the mass of a hypothetical
gauge boson leads to the necessity of introducing at least one new family of heavy fermions. 相似文献