Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973 [12]. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.     

On Epstein’s Trajectory Model of Non-Relativistic Quantum Mechanics

In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).     

Free vibration of antisymmetric,angle-ply laminated plates including transverse shear deformation by the finite element method

A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented. The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. Finite element solutions are presented for rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of a highly anisotropic composite material. Two sets of material properties that are typical of high modulus fiber-reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. The numerical results are compared with the closed form results of Bert and Chen. As a special case, numerical results are presented for thick isotropic plates, and are compared with those for 3-D linear elasticity theory and Mindlin's thick plate theory.     

A complex minkowski space approach to twistors

This paper is basically a review of known results in twistor theory. Its value is intended to lie in the connections presented between twistor concepts and structures in complex Minkowski space. The relationship of twistor theory to complex null infinity and a new proof of the Kerr theorem are presented; these results are to some extent original.     

Does quantum mechanics accept a stochastic support?

Arguments are given in favor of a stochastic theory of quantum mechanics, clearly distinguishable from Brownian motion theory. A brief exposition of the phenomenological theory of stochastic quantum mechanics is presented, followed by a list of its main results and perspectives. A possible answer to the question about the origin of stochasticity is given in stochastic electrodynamics by assigning a real character to the vacuum radiation field. This theory is shown to reproduce important quantum mechanical results, some of which are presented explicitly to illustrate its potentialities. Finally the main problems and some perspectives of research within stochastic electrodynamics are discussed.     

各向同性光波导受到各向同性微扰时的严格矢量耦合模理论

从Maxwell方程出发，推导出各向同性光波导受到各向同性微扰时严格的非正交矢量耦合模理论，在耦合系数的表达式中发现不包含Wei-Ping Huang 的准矢量耦合模理论中的偏振耦合项，但在推导过程中曾出现过偏振耦合项.最后认为这是由于偏振耦合项是二阶小量，而弱导近似忽略了与之相等的二阶小量耦合项.因此,严格的矢量耦合模理论不存在该项而准矢量耦合模理论可把偏振耦合项作为修正项.     

Simultaneous Q-switching and mode-locking in the CW Nd: YAG laser

The theory of transient mode-locking for an active modulator in a laser with a homogeneously broadened line is presented. The theory is applied to simultaneously Q-switched and mode-locked Nd:YAG lasers and good agreement between theory and experiment is obtained. The main conclusion is that under usual Q-switched operating conditions the mode-locking process does not have sufficient time to build up to steady-state conditions. We also present a method to overcome this problem by allowing the laser to prelase before the Q-switch is opened. Mode-locked pulses whose width approaches the steady-state value are obtained. The transient mode-locking theory presented here also applies to actively mode-locking TEA CO₂ lasers and to other types of simultaneously pulsed and mode-locked lasers.     

Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

Statistics of real eigenvalues in Ginibre's ensemble of random real matrices

The integrable structure of Ginibre's orthogonal ensemble of random matrices is looked at through the prism of the probability p(n,k) to find exactly k real eigenvalues in the spectrum of an n x n real asymmetric Gaussian random matrix. The exact solution for the probability function p(n,k) is presented, and its remarkable connection to the theory of symmetric functions is revealed. An extension of the Dyson integration theorem is a key ingredient of the theory presented.     

Pump beam propagation in circular waveguides of optically pumped far-infrared lasers

A theory is presented describing the infrared pump beam propagation in circular waveguides of OPFIRLs. Based upon a ray representation of the Gaussian beam, the overall transport of pump power into the gas by nonlinear absorption and into the wall of the waveguide by partial reflections can be balanced. The theory was used to study the typical pumping conditions in OPFIRL and the main results are presented.     

Theory of collision effects on atomic and molecular line shapes

A review of recent developments in the theory of the effects of binary collisions on the spectral profiles associated with atomic and molecular systems is presented. To consistently account for collisional perturbations of both the internal energy levels and the velocity of active (emitting or absorbing) atoms or molecules, one must use a theory in which the center-of-mass motion of the active atoms has been quantized. Following this procedure general equations for absorption or emission line shapes are obtained. The line shapes may exhibit narrowing or broadening with increasing perturber pressure, depending upon the nature of the collision interaction. The physical significance of the collision mechanisms giving rise to such behavior is discussed, as is the experimental evidence in support of the theory. Various applications of the theory are presented.     

Theoretical description of the spectroscopic properties of rare earth ions in crystals

In this article the present state of knowledge of the theory of one- and two-photon processes observed in rare earth ions in crystals is presented. The conclusions are based on the results of ab initio calculations performed for various ions across the lanthanide series. The model applied for the calculations is based on the Rayleigh–Schrödinger perturbation theory, and the amplitude of a certain electric dipole transition is expressed in terms of effective operators. The radial integrals of the effective operators are defined by the perturbed functions that contain the perturbing influence of single excitations from the 4f shell to all one-electron states of a given symmetry, discrete and continuum. In this approach the interactions between the 4f^N and the excited configurations via the crystal field potential, the electron correlation operator and the spin–orbit interaction operator are discussed; it is believed that the presented theory contains the most important physical mechanisms responsible for the f↔f electric dipole transitions. Two alternative formulations of the theory of one-photon electric dipole transitions are presented. Consequently, the transition amplitude is defined within the standard theory based on the length formula and within a new approach which is based on the velocity form of the electric dipole radiation operator.     

Consistency of isotropic modified Maxwell theory: Microcausality and unitarity

The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A finite domain of positive and negative values of this Lorentz-violating parameter is determined, in which microcausality and unitarity hold. The main focus of this article is on isotropic modified Maxwell theory, but similar results for an anisotropic nonbirefringent case are presented in Appendix A.     

Generalizations of gravitational theory based on group covariance

The mathematical structure, the field equations, and fundamentals of the kinematics of generalizations of general relativity based on semisimple invariance groups are presented. The structure is that of a generalized Kaluza-Klein theory with a subgroup as the gauge group. The group manifold with its Cartan-Killing metric forms the source-free solution. The gauge fields do not vanish even in this case and give rise to additional modes of free motion. The case of the de Sitter groups is presented as an example where the gauge field is tentatively assumed to mediate a spin interaction and give rise to spin motion. Generalization to the conformal group and a theory yielding features of Dirac's large-number hypothesis are discussed. The possibility of further generalizations to include fermions are pointed out. The Kaluza-Klein theory is formulated in terms of principal fibre bundles which need not to be trivial.     

EXAFS spectroscopy,from one perspective

Summary Extended X-ray absorption fine-structure (EXAFS) spectroscopy has been demonstrated to be a most useful probe of short-range interatomic correlations in a wide variety of materials. The theory of the EXAFS is presented in its simplest form so as to provide the basis for a discussion about the kind and quality of the structural information which can be extracted from EXAFS data. The adequacy of several of the approximations commonly incorporated in this theory is examined with emphasis on those areas of the theory which bear most directly on the analysis of EXAFS data. Paper presented at the Workshop on ?EXAFS Data Analysis in Disordered Systems?, held in Parma, October 5–7, 1981.     

Some formal aspects of subdynamics

The theory of subdynamics is formulated assuming the existence of a spectral representation of the collision operator. This approach avoids perturbation schemes; however the presentation is formal. It may be used to develop further the theory as well as a starting point for a rigorous mathematical discussion. The construction of the operators introduced in the theory of subdynamics is presented in detail. Some questions related to the transformation theory leading to the so-called “physical representation” are briefly discussed.