Duality theorems in BRST cohomology

In classical mechanics, there is no duality theorem relating the BRST cohomologies at positive and negative ghost numbers since these generically fail to be isomorphic. It is shown in this paper, however, that a duality theorem for the BRST operator cohomology can be established in quantum mechanics. Furthermore, when the hermicity properties of the quantum BRST formalism—which are in general just formal—turn out to be actually well defined, this duality theorem also holds for the state cohomology, as a consequence of the non degenerate pairing between subspaces at positive and negative ghost numbers defined by the BRST scalar product. In the case of gauge systems quantized in the Schrödinger representation with compact gauge orbits, the duality theorem contains ordinary Poincaré duality for a compact manifold. In the Fock representation, the duality theorem sheds a new light on existing decoupling theorems. The comparison with the classical situation is also briefly discussed.     

Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field

This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner funetion of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain, e.g., the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities—and their spectrum—(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem, on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.     

循环量子系统中状态演化的Bloch定理和同步几何相位的统一

对于Hamiltonian随时间作周期变化的量子系统中状态的演化，Bloch定理亦成立，并可据此定义一种新的几何相位———Bloch相位．证明用这种新的几何相位可以把迄今发现的所有同步（即量子态演化一周后获得的）几何相位统一起来，即Bloch相位等于Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位，并且在绝热条件下化为Bery相位．为此，先对Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位的定义作等价的改变，使它们变得有物理意义，并把Lewis-Riesenfeld相位和Berry相位推广到简并情形．还讨论了Bloch相位的求解问题 关键词：     

The Quantal Canonical Symmetries for a Singular Lagrangian System with Subsidiary Constraints

The quantization for a system containing subsidiary constraints (in configuration space) with a singular Lagrangian is studied, in certain case which can be brought into the theoretical framework of constrained Hamiltonian system. A modified Dirac-Bergmann algorithm for the calculation of all phase-space constraints in those systems is derived. The path integral quantization is formulated by using the Faddeev-Senjanovic scheme. The classical and quantum canonical symmetries (Noether theorem in canonical formalism) are established for such a system. An example is given to illustrate that the connection between the symmetry and conservation law in classical theory are not always validity in the quantum theory.     

Once again on the equivalence theorem

The equivalence theorem in quantum field theory is proven on the basis of the field-antifield formalism. It is shown that the equivalence theorem does not contradict the well-known fact that, in quantum theory, some symmetries of the classical action functional are broken (anomalous). By way of example, a model is considered where natural finite counterterms can be chosen in different ways leading to physically nonequivalent quantum theories, but where the equivalence theorem remains valid.     

Electro-optics of molecules

The natural vibrations and electro-optics of diatomic molecules are considered in the framework of the perturbation theory. The energy of anharmonic vibrations and the matrix of a dipole moment function are determined with allowance made only for nonzero perturbation contributions. In particular, the case of strong electro-optical anharmonicity of diatomic molecules (i.e., the situation where the dipole moment function significantly deviates from linear behavior) is analyzed in the second order of the perturbation theory. Within the introduced formalism of polynomials of the quantum numbers, the perturbation theory is extended to polyatomic molecules and expressions for the matrix elements of the dipole moment are derived in explicit form with due regard for the vibrational quantum numbers.     

Some properties of the moshinsky coefficients

Moshinsky has suggested a method of calculating Talmi transformation coefficients in which the coefficients with two radial quantum numbers equal to zero are calculated first and then recursion formulas over radial quantum numbers are applied. The coefficients with two radial quantum numbers equal to zero are shown to be expressed as factorials, in terms of a particular type of coefficient with all radial quantum numbers equal to zero, and a simple formula for these coefficients is given. Some interesting properties of the Moshinsky coefficient sums are found and a simple formula expressing the coefficients of the “three-body” hyperspherical function transformation in terms of generalized Moshinsky coefficients is obtained. Recursion formulas and symmetry relations for the Moshinsky coefficients are also discussed.     

Formulation of Schrödinger-Like Relativistic Wave Equation of Motion

A Schrödinger-like formalism of relativistic quantum theory is presented based on an alternative Lagrangian formalism of relativistic mechanics with the proper time as the evolution parameter. The Schrödinger-like formalism resolves the great difficulties of negative probability density, Klein paradox, and Zitterbewegung. Ehrenfest's theorem is preserved in the Schrödinger-like formalism.     

Importance of reversibility in the quantum formalism

In this Letter I stress the role of causal reversibility (time symmetry), together with causality and locality, in the justification of the quantum formalism. First, in the algebraic quantum formalism, I show that the assumption of reversibility implies that the observables of a quantum theory form an abstract real C^{?} algebra, and can be represented as an algebra of operators on a real Hilbert space. Second, in the quantum logic formalism, I emphasize which axioms for the lattice of propositions (the existence of an orthocomplementation and the covering property) derive from reversibility. A new argument based on locality and Soler's theorem is used to derive the representation as projectors on a regular Hilbert space from the general quantum logic formalism. In both cases it is recalled that the restriction to complex algebras and Hilbert spaces comes from the constraints of locality and separability.     

组合Bose场的分数自旋和分数统计性

对组合Bose子场，采用FS (Faddeev-Senjanovic) 路径积分量子化方法进行量子化.从量子Noether定理出发，给出量子分数自旋和分数统计性质. 关键词： 路径积分量子化 分数自旋 分数统计     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Intraband absorption of electromagnetic radiation by quantum nanostructures with parabolic confinement potential

The intraband absorption of electromagnetic radiation by two types of nanostructures of cylindrical symmetry—by a quantum cylinder (ring) and a quantum wire—is investigated. Analytical expressions for the coefficients of absorption of high-frequency electromagnetic radiation by the electron gas of nanostructures are obtained. It is shown that the absorption curve exhibits resonance peaks and that, in the case of a degenerate gas, these peaks have breaks.     

The Quantal Symmetries in the Composite Boson's System

The composite Boson's system is quantizated in Faddeev-Senjanovic (FS) path integral quantizated formalism. The canonical Ward identities for proper vertices under local gauge transformation are derived. The fractional spins and fractional statistics are obtained by using the quantum Noether theorem.     

Diode-laser measurements of O2, N2 and air-pressure broadening and shifting of NH3 in the 10 μm spectral region

Using a tunable diode-laser spectrometer, we have measured the O₂, N₂, air-shift and broadening coefficients for 5 lines of ammonia in the R branch of the ν₂ band. These lines are located in the spectral range 1030-1070 cm⁻¹. The pressure shift and broadening are obtained by fitting the measured shapes of these lines by a Voigt profile. The broadening parameters and shift coefficients are compared to the results of theoretical calculations based on the semiclassical Robert-Bonamy formalism (RB) in which the intermolecular potential includes electrostatic, induction, and dispersion energy contributions. The variation of these coefficients with rotational and vibrational quantum numbers is examined. The results are generally in satisfactory agreement with experimental data.     

Quantum Symmetry for a System with a Singular Lagrangian Containing Subsidiary Condition

The quantization for a system with a singular Lagrangian containing subsidiary constrained conditions in configuration space is studied. The system is called constrained singular system. In certain case, the constrained singular system can be brought into the theoretical framework of the constrained Hamilton system. A modified Dirac-Bergmann algorithm for the calculation of constraints in the system is deduced. The path integral quantization is formulated by using the Faddeev-Senjanovic scheme, and the classical/quantum Noether theorem in canonical formalism are also established for such a system. The application of the results to study the fractional spin in non-Abelian Chern-Simons theory is given. We make a precise investigation of the fractional spin for such a system at the quantal level. A simple example is presented to show that the connection between the symmetry and conservation law in classical theories in general is no longer preserved in quantum theories.     

Are there basic laws of quantum information processing?

We prove within the quantum formalism without reduction postulate that the no-cloning theorem and the principle of no-increasing of entanglement (in a bit weaker formulations) are equivalent. We argue that the result is a manifestation of more general principles governing quantum information processing analogous to the thermodynamical laws.     

Brownian motion of a quantum harmonic oscillator

The problem of describing the Brownian motion of a quantum harmonic oscillator or free particle is treated in the formalism of quantum dynamical semigroups. Certain inequalities involving the friction and diffusion coefficients and Planck's constant are derived. The nature of the quantum Langevin equation is discussed.     

Star products and geometric algebra

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficients of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.     

Morse势阱中子带间的光吸收

研究了Morse势阱中子带间的光吸收,并且利用密度矩阵算符理论和迭代方法,推导出了线性和三阶非线性子带间的光吸收系数的解析表达式,然后以GaAs/AlGaAsMorse势阱为例进行数值计算。结果表明,线性吸收系数是正的,为总吸收系数作出积极的作用,而三阶非线性吸收为负,抵消了一部分线性吸收,进而得到总的吸收系数;吸收系数随着入射光强度的增大而减小,即出现吸收饱和现象;当势阱参数a增大时,吸收系数增大,即阱宽较窄时,系统吸收的能量较多。若要获得较大的光学吸收系数,就要输入较小的光场强度,并选择适当的势阱参数a和入射光频率。     

Functional approach to scattering in quantum field theory

A functional approach to scattering theory in quantum field theory is developed by deriving an explicit functional expression fortransition amplitudes. In applications, the formalism avoids dealing with noncommutativity problems of field operators, avoids solving the field equations, avoids dealing with the often quite complicated continual (path) integrals, and avoids combinatoric problems associated with Feynman rules and the old-fashioned Wick's theorem. Finally, it avoids explicitly taking mass shell limits as in the LSZ formalism. The basic idea of the formalism is to use the quantum action principle followed by a systematic analysis of the concept of stimulated emissions as applied to particles of any spin, and is a generalization of an earlier method applied by the author to the much simpler situation of quantum mechanics.