Extension of the Chern–Simons Theory: Conservation Laws,Lagrange Structures,and Stability

Russian Physics Journal - We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern–Simons operator. For the nth order theory of...     

复合函数算符的微商法则及其在量子物理中的应用

给出了在量子物理学、量子统计学、算符排序理论、矩阵论以及控制理论中有着重要用途的复合函数算符的一般微分法则,利用这一法则研究了Wigner算符和Weyl对应规则中的积分问题,证明了两类典型的算符恒等公式.给出了Wigner算符的有序算符内的微分形式,并得到了一些重要函数的新的微分式.最后,引入了一个参数型的Wigner算符来统一正规序、Weyl编序以及反正规序三种算符排序.     

Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan–Paton factor is given by a trace over elements of Poincaré algebra and Iwahori–Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan–Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.     

Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to hyperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution---a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.     

Theory of q-deformed forms. III. q-deformed Hodge star,inner product,adjoint operator of exterior derivative,and self-dual yang-mills equation

In this paper we introduce the q-deformed Hodge star operator, q-deformed inner product, and q-deformed adjoint of the q-deformed exterior derivative and investigate their properties. Using this mathematical background, we construct the q-deformed self-dual Yang-Mills theory.     

An Operator Method of the Theory of Optical Coherence and Radiometry

This paper presents a quantum mechanical formalism of the classical coherence theory, within which the generalized radiance function defined in the time domain is regarded as a phase space representative of a time-dependent correlation operator of a polychromatic field. The theory deals with both stationary and nonstationary fields and, for a stationary field, provides a new operator formalism of the usual theory of optical coherence developed in the space-frequency domain. New results include an operator representation of the mutual coherence function, an operator version of the Wiener-Khintchine theorem, and an operator theorem that projects the correlation operator of a polychromatic field onto a particular spectral component. As illustrative examples, the previous formulas regarding the relationship between temporal coherence and spatial coherence, and the relationship between spectral properties and coherence properties are derived from the new operator formulas. The correspondence of the present formalism to the usual formalism using Dirac notation to describe the propagation of a stationary, partially coherent, quasi-monochromatic field is also considered.     

Asymptotic Spectral Measures, Quantum Mechanics, and E-Theory

We study the relationship between POV-measures in quantum theory and asymptotic morphisms in the operator algebra E-theory of Connes–Higson. This is done by introducing the theory of “asymptotic” PV-measures and their integral correspondence with positive asymptotic morphisms on locally compact spaces. Examples and applications involving various aspects of quantum physics, including quantum noise models, semiclassical limits, strong deformation quantizations, and pure half-spin particles, are also discussed. Received: 27 December 2000 / Accepted: 8 October 2001     

Distortion operator approach and [N, 1] Padé sequence in nonrelativistic scattering theory

A brief account of the scattering theory using the so called distortion operator is given. The Neumann series for a matrix element of the distortion operator is proved to imply the [N, 1] Padé sequence for the transition matrix element. As a consequence a region of convergence of the [N, 1] Padé sequence is found.     

Entropy of nonrotating isolated horizons in Lovelock theory from loop quantum gravity

In this paper,the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory.The final entropy matches the Wald entropy formula for this theory.We also confirm the conclusion obtained by Bodendorfer et al.that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.     

Explicit Expression of Seniority Particle Operator and Its Properties in Quasi-spin Theory

The explicit expression of the seniority particle operator and its properties in the quasi-spin theory of nuclear physics is presented in this paper. The seniority particle operator can be used to construct D-pair in the microscopic theory of interacting boson model to avoid the seniority mixing problem.     

Relative Oscillation Theory,Weighted Zeros of the Wronskian,and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm–Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein’s spectral shift function is established. Research supported by the Austrian Science Fund (FWF) under Grant No. Y330.     

Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III

Quantum geometry, algebras with nonlinear commutation relations, representation theory, the coherent transform, and operator averaging are used to solve the perturbation problem for wave (quantum) systems near a resonance equilibrium point or a resonance equilibrium ray in two and three-dimensional spaces. This work was partially supported by RFBR (grant 05-01-00918-a).     

Explicit Expression of Seniority Particle Operator and Its Properties in Quasi-spin Theory

The explicit expression of the seniority particle operator and its properties in the quasi-spin theory of nuclear physics is presented in this paper. The seniority particle operator can be used to construct D-pair in the microscopic theory of interacting boson model to avoid the seniority mixing problem.     

Scalar quantum field theory with a complex cubic interaction

In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.     

Monopoles, vortices and confinement in SU(3) gauge theory

We compute, in SU(3) pure gauge theory, the vacuum expectation value (VEV) of the operator which creates a Z₃ vortex wrapping the lattice through periodic boundary conditions (dual Polyakov line). The technique used is the same already tested in the SU(2) case. The dual Polyakov line proves to be a good disorder parameter for confinement, and has a similar behaviour to the monopole condensate. The new features which characterise the construction of the disorder operator in SU(3) are emphasised.     

描述高自旋弱耦合系统的广义积算符

本文提出了Z算符与角动量积算符相结合的广义积算符,用于描述高自旋弱耦合系统NMR实验谱。给出了高自旋系统在自旋耦合作用下的演变公式,Z算符在脉冲作用下的变化公式。以氘(D)为例,计算了重聚INEPT,DEPT和同核COSY实验谱,并对计算方法作了讨论。     

Determination of singularities in an operator of partial radiation conditions

The structure of an operator that determines the partial conditions of radiation in the scalar problem of diffraction theory is considered. Nonlocal boundary conditions are determined by a series setting a certain integro-differential operator. The principal part of this operator is presented in the explicit form of a hyper-singular operator and its components with lower-order singularities. The remaining rapidly converging part of the functional series determines an integral operator with a continuous kernel.     

An interpretation of noncommutative field theory in terms of a quantum shift

Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.