共查询到20条相似文献,搜索用时 31 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.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
3.
D. Kastler M. Mebkhout G. Loupias L. Michel 《Communications in Mathematical Physics》1972,27(3):195-222
With
aC*-algebra with unit andgG
g
a homomorphic map of a groupG into the automorphism group ofG, the central measure
of a state of
is invariant under the action ofG (in the state space of
) iff is -invariant. Furthermore if the pair {
,G} is asymptotically abelian, is ergodic iff
is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on
, the associated covariant representations of {
, } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states. 相似文献
4.
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
5.
For the non-compact abelian lattice Higgs model in Landau gauge Kennedy and King (Princeton preprint, 1985) showed that the two point function
does not decay in the Higgs phase. We generalize their methods to show that for the same range of parameters there are states parametrized by an angle [0, 2) such that
and
0$$
" align="middle" border="0">
. 相似文献
6.
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
7.
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
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.
František Katrnoška 《International Journal of Theoretical Physics》1995,34(8):1501-1505
The notions of the left (right) Jordan groupoids are introduced. IfR is an associative* ring with the identity and ifU(R) [resp.P(R)] denotes the set of all idempotents (resp. projections) of the* ringR, then the operationsp
q =p – 2pq – qp + 4qpq andp
q =q – 2pq – 2qp + 4pqp ifp, q U(R) [resp.p, q P(R)] are the nonassociative linear operations inU(R) [resp. inP(R)]. The present paper shows that the operations
and
are associative iffpq=qp forp, q U(R) [resp.p, q P(R)]. As a corollary it follows from this that the orthomodular poset (U(R), , 0, 1,) is a Boolean algebra [which is commutative, i.e.,pq= qp, p, q U(R)] iff (U(R),
, 0, 1,) or (U(R),
, 0, 1,) are Jordan associative groupoids. Similar results hold for (P(R), ,0, 1, ). 相似文献
10.
In this Letter we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a constant volume form and a Poisson bivector field on
d
such that div=0, the Kontsevich star product with the harmonic angle function is cyclic, i.e.
(f*g)·h·=
(g*h)·f· for any three functions f,g,h on
(for which the integrals make sense). We also prove a globalization of this theorem in the case of arbitrary Poisson manifolds and an arbitrary volume form, and prove a generalization of the Connes–Flato–Sternheimer conjecture on closed star products in the Poisson case. 相似文献
11.
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
12.
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
13.
Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant
coming from non-observability of 0 in 76Ge are found. The dependence of
on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that
strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment. 相似文献
14.
H. C. Hsieh 《International Journal of Infrared and Millimeter Waves》1981,2(1):131-147
The expression for free carrier Faraday rotation and for ellipticity , as the function of the applied parallel static electric field
and static magnetic field
for a given value of wave angular frequency and electron concentration N0, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as
, where
,
, and
. Here m* and e denote the effective mass and charge of electron, respectively. g is the forbidden bandgap of semiconductor. v0 is the carrier drift velocity, which is a non-linear function of E0 in high field condition. A possibility of a simple way of determining the non-linear v0 vs E0 characteristics of semiconductors by the measurement of Faraday rotation is also discussed. 相似文献
15.
On the Schrödinger equation and the eigenvalue problem 总被引:1,自引:0,他引:1
If
k
is thek
th eigenvalue for the Dirichlet boundary problem on a bounded domain in
n
, H. Weyl's asymptotic formula asserts that
, hence
. We prove that for any domain and for all
. A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on
n
(n3) in terms of
is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1 相似文献
16.
Toshiharu Kawai 《General Relativity and Gravitation》1986,18(10):995-1018
We develop a gauge theory of gravity on the basis of the principal fiber bundle over the four-dimensional space-timeM with the covering groupP¯
0
of the proper orthochronous Poincaré group. The field components
are constructed with the connection coefficients
,
and with a Higgs-type field. A Lorentz metricg is introduced with
, which are then identified with the components of duals of the Vierbein fields. Associated with there is a spinor structure onM. For Lagrangian densityL, which is a function of
,
,, matter field , and oftheir first derivatives, we give the conditions imposed by the requirement of the
gauge invariance. The Lagrangian densityL is restricted to be of the formL =L
tot
(, T
klm
,R
klmn
,
k
, ), in whichT
klm
,R
klmn
are the field strengths of
,
, respectively. Identities and conservation laws following from the
gauge invariance are given. Particularly noteworthy is the fact that the energy momentum conservation law follows from theinternal translational invariance. The field equation of is automatically satisfied, if those of
and of are both satisfied. The possible existence of matter fields with intrinsic energy momentum is pointed out. When is a field with vanishing intrinsic energy momentum, the present theory practically agrees with the conventional Poincaré gauge theory of gravity, except for the seemingly trivial terms in the expression of the spin-angular momentum density. A condition leading to a Riemann-Cartan space-time is given. The field holds a key position in the formulation. 相似文献
17.
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
18.
Models of random systems whose Hamiltonian reads
, where
and
i
,=1,...,n are independent, identically distributed random variables are discussed.J
ij
are assumed to be symmetric, with respect toJ
0, random variables and also symmetric functions of components of
. A question of dependence of a phase diagram on a probability distribution of
is addressed. A class of distributions and interactionsJ
ij
, which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied. 相似文献
19.
S. Doplicher R. V. Kadison D. Kastler Derek W. Robinson 《Communications in Mathematical Physics》1967,6(2):101-120
We study pairs {
, } for which
is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of
. We examine, especially, those systems {
, } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A
g
(B) —
g
(B)A 0 asg for those states such that (
g
(A)) = (A) for allg inG andA in
). For concrete systems (those with
-acting on a Hilbert space andg
g
implemented by a unitary representationg U
g
on this space) we prove, among other results, that the operators commuting with
and {U
g
} form a commuting family when there is a vector cyclic under
and invariant under {U
g
}. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of {
,U
g
}. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics. 相似文献
20.
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