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1.
We define and analyze Lipschitz spaces ,q associated with a representationxgV(x) of the Lie algebrag by closed operatorsV(x) on the Banach space together with a heat semigroupS. If the action ofS satisfies certain minimal smoothness hypotheses with respect to the differential structure of (,g,V) then the Lipschitz spaces support representations ofg for which productsV(x)V(y) are relatively bounded by the Laplacian generatingS. These regularity properties of the ,q can then be exploited to obtain improved smoothness properties ofS on . In particularC 4-estimates on the action ofS automatically implyC -estimates. Finally we use these results to discuss integrability criteria for (,g,V).Dedicated to Res Jost and Arthur Wightman  相似文献   

2.
Given two unital C*-algebrasA, and their state spacesE A , E respectively, (A,E A ) is said to have (, E) as a hidden theory via a linear, positive, unit-preserving map L: A if, for all E A , L* can be decomposed in E into states with pointwise strictly less dispersion than that of . Conditions onA and L are found that exclude (A,E A ) from having a hidden theory via L. It is shown in particular that, ifA is simple, then no (, E) can be a hidden theory of (A,E A ) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra such that (, E) is a hidden theory of (A,E A ) via a conditional expectation from ontoA.  相似文献   

3.
Learning of patterns by neural networks obeying general rules of sensory transduction and of converting membrane potentials to spiking frequencies is considered. Any finite number of cellsA can sample a pattern playing on any finite number of cells without causing irrevocable sampling bias ifA = orA =. Total energy transfer from inputs ofA to outputs of depends on the entropy of the input distribution. Pattern completion on recall trials can occur without destroying perfect memory even ifA = by choosing the signal thresholds sufficiently large. The mathematical results are global limit and oscillation theorems for a class of nonlinear functional-differential systems.The preparation of this work was supported in part by the National Science Foundation (GP 9003), the Office of Naval Research (N00014-67-A-024-OQ16), and the A.P. Sloan Foundation.  相似文献   

4.
We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.  相似文献   

5.
A system of coordinates on a set of selfdual lattices in a two-dimensionalp-adic symplectic space (V,) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,) depending on a lattice (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices one defines the Maslov index =(1,2,3) of a triple of lattices. Properties of the index are investigated and values of in coordinates for different triples of lattices are calculated.  相似文献   

6.
ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent A A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent S : monotonicity, concavity,w* upper semicontinuity, etc.  相似文献   

7.
It is proved that the monotone -closure of the self-adjoint part of anyC*-algebraA is the self-adjoint part of aC*-algebra . IfA is of type I it is proved that is weakly -closed, i.e. is a*-algebra. The physical importance of*-algebras was explained in [1] and [7].  相似文献   

8.
We study the monodromy representations k,Iof the mapping class group 4 acting on 4-point blocks satisfying the Knizhnik-Zamolodchikov equation for the levelk su2 current algebra. We classify all irreducible k,Iwhich are realized by finite groups; we also display finite irreducible components for the reducible representations corresponding tok = 10.Supported by the Federal Ministry of Science and Research, Austria.  相似文献   

9.
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   

10.
This paper answers the open question 1 of [3] in the affirmative and, conditionally, the open question 2 of [3], too. Assuming irreducibility of the orthomodular latticeG of all physical decision effectsE, we shall prove in the first section that modularity ofG implies symmetry of the physical probability function . In the second section, we shall consider the filter algebra (B) being assumed to possess an involution * such thatT*T=0 impliesT=0. Then this will be proved: If every atomic filterT P is a fixpoint of * and * is, in a restricted manner, norm-preserving on the minimal left ideal P :=(B)T P , thenG is modular.  相似文献   

11.
Let 1(x) and 2(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution 1(x)2(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that 1(x)2(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft  相似文献   

12.
Iff is a rational map of the Riemann sphere, define the transfer operator by Let also be the Banach space of functions for which the second derivatives are measures. Ifg andg satisfies a simple integrability condition (implying thatg vanishes at critical points and multiple poles off) then is a bounded linear operator on . The essential spectral radius of can be estimated and, under suitable conditions, proved to be strictly less than the spectral radius. Similar estimates for more general operators are also obtained.  相似文献   

13.
Størmer proved a theorem on the integral decomposition of symmetric states on a C *-algebra . Motivated by problems in statistical mechanics, we define summetric states on a composite algebra A ( )and extend Størmer's theorem to this situation. Applications to spin-boson models are sketched.  相似文献   

14.
Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.  相似文献   

15.
ParisA of local quantum field theories are studied, whereA is a chiral conformal quantum field theory and is a local extension, either chiral or two-dimensional. The local correlation functions of fields from have an expansion with respect toA into conformal blocks, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: (a) by constructing the monodromy representation of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and (b) by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.  相似文献   

16.
We deal with quantum field theory in the restriction to external Bose fields. Let be the Dirac equation. We prove that a nonquantized Bose field is a functional of the Dirac field whenever this is canonical. Performing the verification for := m = const, which yields the free Dirac field, we also prepare the tedious verifications for all which are nonquantized and static. Such verifications must not be confused, however, with the proof of our formula, which is shown in detail.  相似文献   

17.
Consider a two-rooted graphG, the edges of which are directed in such a way that there are no cycles and every edge belongs to some self-avoiding walk from rootu to rootv which follows the direction of the edges. Au-v backbone ofG is a subgraph formed by taking the union of any subset of directed self-avoiding walks fromu tov. Let uv be the set of all such backbones ofG partially ordered by set-inclusion. We prove the conjecture of Bhatti and Essam that the Möbius function of this set is given, for acyclicb,b uv withbb, by(b,b)=(–1) c-c , wherec andc are the respective cycle ranks ofb andb. The significance of this result in percolation theory is reviewed together with previous results for other sets of subgraphs.  相似文献   

18.
We fit the CKM-matrix to all recent data with the following free parameters: three mixing angles, the CP-violating angle in the Maiani parametrisation, the top quark massm t, and the productf B B0 1/2 , wheref B is theB-meson decay parameter and B 0 is the bag parameter. Our fits span a contiguous region in the (f B B0 1/2 , cos )-plane. The parametersf B B0 1/2 and cos are strongly positively correlated.  相似文献   

19.
LetH=–+V+Fx 1 withV(x 1,x ) analytic in the first variable andV(x 1+ia, x ) bounded and decreasing to zero asx for eacha . Let be an eigenvector of –+V with negative eigenvalue. Among our results we show that forF0, (,e H ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to conventional atomic resonances for which power law decay is the rule.Research supported by NSF Grant No. MCS 78-00101.  相似文献   

20.
We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* p 2aX p . Also, for any two operatorsA andB, AB 2 2 +A*B* 2 2 2AB 2 2 .  相似文献   

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