Higher order estimates for the Yukawa2 quantum field theory

Uniqueness of KMS states is proved for one-dimensional quantum lattice system. Sakai's theorem on uniqueness of KMS states is generalized to cases of non-commutative generators.     

Diffractive parton distributions from the saturation model

We review diffractive deep inelastic scattering (DIS) in the light of the collinear factorization theorem. This theorem allows one to define diffractive parton distributions in the leading twist approach. Due to its selective final states, diffractive DIS offers interesting insight into the form of the diffractive parton distributions which we explore with the help of the saturation model. We find Regge-like factorization with the correct energy dependence measured at HERA. A remarkable feature of diffractive DIS is the dominance of the twist-4 contribution for small diffractive masses. We quantify this effect and make a comparison with the data. Received: 22 February 2001 / Revised version: 22 March 2001 / Published online: 3 May 2001     

Geometric quantization of symplectic manifolds with respect to reducible non-negative polarizations

The leafwise complex of a reducible non-negative polarization with values in the prequantum bundle on a prequantizable symplectic manifold is studied. The cohomology groups of this complex is shown to vanish in rank less than the rank of the real part of the non-negative polarization. The Bohr-Sommerfeld set for a reducible non-negative polarization is defined. A factorization theorem is proved for these reducible non-negative polarizations. For compact symplectic manifolds, it is shown that the above complex has finite dimensional cohomology groups, more-over a Lefschetz fixed point theorem and an index theorem for these non-elliptic complexes is proved. As a corollary of the index theorem, we deduce that the cardinality of the Bohr-Sommerfeld set for any reducible real polarization on a compact symplectic manifold is determined by the volume and the dimension of the manifold. Supported in part by NSF grant DMS-93-09653, while the author was visiting University of California Berkeley.     

Phenomenon of mobility in non-linear theories

Homeomorphisms of the unit-sphere of states are studied. Generalizations of the Piron statement and Wigners' theorem are obtained. It is shown that if the semigroup of the unitary operations of quantum theory were extended by introducing any non-linear operation, amobility phenomenon would occur consisting of a possibility of moving any two states to any two surroundings on the unit sphere. For the resulting non-linear wave packets the complementarity doctrine would become impossible because of fluidity of the space of states under the dynamical transformations.Supported by COSNET/SEPOn leave of absence from Institute of Physics, Warsaw University, Warsaw, Poland     

The quantum mechanics of affine variables

We study the wrapping of N-type IIB Dp-branes on a compact Riemann surface Σ in genus g>1 by means of the Sen–Witten construction, as a superposition of N′-type IIB Dp′-brane/antibrane pairs, with p′>p. A background Neveu–Schwarz field B deforms the commutative C-algebra of functions on Σ to a non-commutative C-algebra. Our construction provides an explicit example of the N′→∞ limit advocated by Bouwknegt-Mathai and Witten in order to deal with twisted K-theory. We provide the necessary elements to formulate M(atrix) theory on this new C-algebra, by explicitly constructing a family of projective C-modules admitting constant-curvature connections. This allows us to define the g>1 analogue of the BPS spectrum of states in g=1, by means of Donaldson’s formulation of the Narasimhan–Seshadri theorem.     

BRST model for equivariant cohomology and representatives for the equivariant thom class

In this paper the BRST formalism for topological field theories is studied in a mathematical setting. The BRST operator is obtained as a member of a one parameter family of operators connecting the Weil model and the Cartan model for equivariant cohomology. Furthermore, the BRST operator is identified as the sum of an equivariant derivation and its Fourier transform. Using this, the Mathai-Quillen representative for the Thom class of associated vector bundles is obtained as the Fourier transform of a simple BRST closed element.Supported by the SV FOM/SMC Mathematical Physics, The Netherlands     

Proof of factorization using background field method of QCD

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof.     

Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non-commutative differential geometry to quantum deformations of a class of Kähler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute an explicit formula for the Chern character on generators of the Toeplitz ^*-algebra.Supported in part by the National Science Foundation under grant DMS-9206936Supported in part by the Department of Energy under grant DE-FG02-88ER25065Supported in part by the Consiglio Nazionale delle Ricerche (CNR)     

Gap Labelling and the Pressure on the Boundary

In quantum systems described by covariant families of 1-particle Schrödinger operators on half-spaces the pressure on the boundary per unit energy is topologically quantised if the Fermi energy lies in a gap of the bulk spectrum. Its relation with the integrated density of states can be expressed in an integrated version of Streda’s formula. This leads also to a gap labelling theorem for systems with constant magnetic field. The proof uses non-commutative topology.     

Generalization of the Levinson Theorem on the Asymptotic Value of the Scattering-Amplitude Phase Shift

Physics of Atomic Nuclei - The Levinson theorem relates the difference of the phase shifts at the threshold and at infinity to the number of bound states. The theorem is modified in view of the...     

On the classical dynamics of charges in non-commutative QED

Following Wongs approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space.Received: 29 October 2003, Revised: 21 April 2004, Published online: 15 June 2004A.H. Fatollahi: Address after March 2004: Department of Physics, Alzahra University, Tehran, 19938-91167, Iran     

Wigner Functions for Klein-Gordon Oscillators in Non-commutative Space

As a quasi-probability distribution function in phase-space and as well as a special representation of the density matrix, the Wigner function is of great significance in Physics. This letter first makes a review of Wigner function and then provides three approaches of calculating it in non-commutative space. Finally, with the help of Moyal-Weyl multiplication and Bopp’s shift, the Wigner functions for Klein-Gordon oscillators in non-commutative space are deduced explicitly.     

Finite de Finetti theorem for infinite-dimensional systems

We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.     

A Formality Theorem for Poisson Manifolds

Letters in Mathematical Physics - Let M be a differential manifold. Using different methods, Kontsevich and Tamarkin have proved a formality theorem, which states the existence of a Lie...     

The optical theorem,a purity of the initial states and the rising total cross-sections

A possibility of the violation of the optical theorem at high energies due to the mixed character of the initial states is discussed. A close connection of this idea with the MIT —bag model of hadrons is shown. The experimental evidence for the validity of the optical theorem is doubted. A plan of the investigations which could lead to the discovery of the optical theorem violation for strong interactions is presented.Supported in part by NSF Grant GF 41958. Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.Editorial note: The paper is getting on to speculative ground. Any speculation is, however, unconvincing.     

Exact solution for the diffusion in bistable potentials

We solve analytically the Fokker-Planck equation for a one-parameter family of symmetric, attractive, nonharmonic potentials which include double-well situations. The exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density. In particular, for the bistable potentials, we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni- to bimodal probability densities.On leave from the Department of Theoretical Physics, Université de Genève, CH-1211, Genève 4, Switzerland.Supported by the Swiss National Fund for Scientific Research.On leave from the Institute of Theoretical Physics, Academia Sinica, Beijing, China.Supported in part by the Robert A. Welch Foundation.     

Gibbons-Maeda dilaton黑洞的全息熵

依据全息原理,通过计算Gibbons-Maeda dilaton黑洞事件视界上量子场的统计熵,得到了该黑洞的全息熵和Bekenstein-Hawking熵.计算中利用非对易量子场论,克服了普通量子场论中态密度在视界上的发散困难,避免了黑洞熵热气体方法中紫外截断的引入.用留数定理克服了计算中的积分困难,所得的结果定量成立.研究表明,黑洞熵可以视为其视界上量子场的熵;通过计算视界上量子态的统计熵可以得到黑洞熵,计算中可以且应该避免视界外量子态的影响. 关键词： 黑洞熵 全息原理 事件视界 非对易量子场论     

A criterion for flatness in minimal area metrics that define string diagrams

It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yieds a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set,U if there is a unique closed curve of length 2 through every point inU and all of these closed curves are in the same free homotopy class.Supported in part by funds provided by the US Department of Energy (DOE) under contract # DE-AC02-76ER03069     

Hidden variables and Bell's theorem in quantum mechanics

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part A_r of a W^*-algebra A (of the most general type) and the states are represented by the normal states (in the mathematical sense) of A. We then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W^*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries).     

Free Meixner States

Free Meixner states are a class of functionals on non-commutative polynomials introduced in [Ans06]. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construct an operator model for free Meixner states. By combinatorial methods, we also derive an operator model for their free cumulant functionals. This, in turn, allows us to construct a number of examples. Some of these examples are shown to be trivial, in the sense of being free products of functionals which depend on only a single variable, or rotations of such free products. On the other hand, the multinomial distribution is a free Meixner state and is not a product. Neither is a large class of tracial free Meixner states which are analogous to the simple quadratic exponential families in statistics. This work was supported in part by NSF grant DMS-0613195.