共查询到20条相似文献,搜索用时 593 毫秒
1.
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
2.
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
3.
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
4.
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
5.
C denotes either the conformal group in 3+1 dimensions, PSO(4, 2), or in one chiral dimension, PSL(2,
). Let U be a unitary, strongly continuous representation of C satisfying the spectrum condition and inducing, by its adjoint action, automorphisms of a von Neumann algebra
. We construct the unique inner representation
of the universal covering group of C implementing these automorphisms.
satisfies the spectrum condition and acts trivially on any U-invariant vector. This means in particular: Conformal transformations of a field theory having positive energy are weak limit points of local observables. Some immediate implications for chiral subnets are given. We propose the name Borchers–Sugawara construction. 相似文献
6.
We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to
, and satisfies
, for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is
, provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B
n
, such that for all B>B
n
, the almost sure spectrum is pure point at all energies
except in intervals of width
about each lower Landau level
, for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE
n
(B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials. 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 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
9.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra
) and use it in examples such as
and
. We also give a sufficient condition on the isotropy subalgebra of
so that the transverse Poisson structureto the coadjoint orbit of is linear. 相似文献
10.
PL. Muthuramalingam 《Letters in Mathematical Physics》1982,6(4):303-307
Let
be the selfadjoint operator for the static electromagnetic field where W
j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H
0). 相似文献
11.
If
(V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V
1
and V
2
are spacelike separated spacetime regions, then the system (
(V
1
),
(V
2
), ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A
(V
1
), B
(V
2
) correlated in the normal state there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V
1
and V
2
and disjoint from both V
1
and V
2
, a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (
(V
1
),
(V
2
), ) with a locally normal and locally faithful state and suitable bounded V
1
and V
2
satisfies the Weak Reichenbach's Common Cause Principle. 相似文献
12.
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
13.
A. Angeletti 《Letters in Mathematical Physics》1980,4(6):495-504
Let (x) be the Dirac's delta,q(x)L
1
(R)L
2
(R) be a real valued function, and , R; we will consider the following class of one-dimensional formal Schrödinger operators on
. It is known that to the formal operator
may be associated a selfadjoint operatorH(,) onL
2(R). Ifq is of finite range, for >0 and || is small enough, we prove thatH(,) has an antibound state; that is the resolvent ofH(,) has a pole on the negative real axis on the second Riemann sheet.Work done while the author was supported by an undergraduate fellowship of the (Italian) National Research Council (CNR). 相似文献
14.
In this Letter, we explicitly classify all modular invariant partition functions for
at levels 2 and 3. Previously, these were known only for level 1. Level 2 exceptions exist at r=9, 15, and 27;level 3 exceptions exist at r=4, 8, and 20. One of these is new, but the others were all anticipated by the rank-level duality relating
level k and
level r+1. The main recent result which this Letter rests on is the classification of
-type invariants. 相似文献
15.
We study the Leibniz homology of the Poisson algebra of polynomial functions over (2n
,) where is the standard symplectic structure. We identify it with certain highest-weight vectors of some
2n
(
)-modules and obtain some explicit result in low degree. 相似文献
16.
The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra
of acyclic arrow graphs (modulo an oriented version
of the STU relation). The algebra
encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented
and
relations hold, and that
is isomorphic to the algebra
of arrow diagrams. As an application, we consider an appropriate link-homotopy version
of the algebra
. Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra
and in . We observe that this construction gives the universal Milnor's link-homotopy -invariants. 相似文献
17.
Wang Zheng Dong 《Letters in Mathematical Physics》1996,38(4):377-388
By considering the cohomology of the loop algebraL
, a representation ofL
is constructed. the construction is based on a derivation ofL
and a two-dimensional closed cochain ofl
with coefficients in real numbersR
1. In the case of =0, the differential of the energy representation of the corresponding loop groupLG is derived.This work was supported in part by the National Natural Science Foundation of China. 相似文献
18.
19.
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra
, let
be the vector space of tensors over
equipped with the Itô Hopf algebra structure derived from the associative multiplication in
. It is shown that a necessary and sufficient condition that the double product integral
satisfy the quantum Yang–Baxter equation over
is that
satisfy the same equation over the unital associative algebra
got by adjoining a unit element to
. In particular, the first-order coefficient r1 of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of
is
where
is the inverse of
in
we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on
in the unital associative subalgebra of
consisting of formal power series whose zero order coefficient lies in the space
of symmetric tensors. The deformation coproduct acts on
by conjugating the undeformed coproduct by
and the coboundary structure r of
is given by
where
is the flip.Mathematical Subject Classification (2000). 53D55, 17B62 相似文献
20.
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