Third-order equation for bispinors

We present the general features of a bispinor field that obeys a third-order equation. It separates into two massive fields that obey the Dirac equation and a four-component massless field. We discuss briefly its electromagnetic interactions and a leptonic interaction that introduces a mass difference. This field can thus describe the electron, the muon and both neutrinos. The difficulties related to inconsistencies between electromagnetic and weak interactions for the two-component spinors are still present for the bispinor field.     

The classical spin-1/2 tachyon field

We present the classical theory of a set of two spinor fields patterned closely after the Dirac theory in two-component form, but each field obeys a modified Klein-Gordon equation, in which the sign ofm ² has been changed. The solution contains parts with real and imaginary frequencies, that contribute differently to conserved quantities such as the charge and the energy-momentum vector. We also show how the minimal interaction with the electromagnetic field is obtained.     

Pauli equation for a particle in metric and electromagnetic fields

A Pauli theory (Pauli equation and definition of probability current and density) for a particle in weak metric and arbitrary electromagnetic fields is treated. To formulate non-relativistic quantum mechanical problems in arbitrary electromagnetic fields and weak metrics (non-inertial systems, gravitational fields which are distant fields of arbitrary distribution of masses, gravitational waves) it is not necessary to make use of the general-relativistic Dirac equation. Close analogies to the known Pauli theory with electromagnetic fields exist. For different metric fields the corresponding Hamiltonians are given. For quantum systems (H-atoms) which are disturbed by a homogeneous gravitational field and a gravitational wave the resulting shift of energy levels and the transition probability is calculated.     

Gravity and the quantum vacuum inertia hypothesis

In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero‐point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum inertia hypothesis . To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero‐point field contributing to the inertial mass of a particle or object.     

Quantum Kinetic Theory for Laser Plasmas. Dynamical Screening in Strong Fields

A quantum kinetic theory for correlated charged-particle systems in strong time-dependent electromagnetic fields is developed. Our approach is based on a systematic gauge-invariant nonequilibrium Green's functions formulation. Extending our previous analysis [1] we concentrate on the selfconsistent treatment of dynamical screening and electromagnetic fields which is applicable to arbitrary nonequilibrium situations. The resulting kinetic equation generalizes previous results to quantum plasmas with full dynamical screening and includes many-body effects. It is, in particular, applicable to the interaction of dense plasmas with strong electromagnetic fields, including laser fields and x-rays. Furthermore, results for the modification of the plasma screening and the longitudinal field fluctuations due to the electromagnetic field are presented.     

Space-time structure of weak and electromagnetic interactions

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the Weinberg-Salam theory of weak and electromagnetic interactions. It follows that internal symmetries of the weak interactions can be interpreted as space-time symmetries of spinor fields in the Dirac algebra. The possibilities for interpreting strong interaction symmetries in a similar way are highly restricted.     

Thomson scattering induced by gravitational waves

We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically, as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization.     

Indefinite charge for the classical spinor field

We define a conserved Lorentz vector for a two-component spinor field that obeys the Klein-Gordon equation and interpret it as a charge-current density. The corresponding total charge can take negative as well as positive values, which is not the case for the usual charge of the Dirac field. We consequently can define probability amplitudes for a relativistic quantum mechanics, and we solve the inhomogeneous equation by means of the causal Green function. This vector is not invariant under gauge transformations of the spinor field, and we cannot generalize the equation by the gauge invariant substitution to obtain the interaction with an electromagnetic field. In the limit of a massless field that obeys the Weyl equation, the charge vanishes.     

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincaré invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark?Cantiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space?Ctime hyperboloid could be advantageous.     

High Intensity Generation of Entangled Photons in a Two‐Mode Electromagnetic Field

At present, the sources of entangled photons have a low rate of photon generation. This limitation is a key component of quantum informatics for the realization of such functions as linear quantum computation and quantum teleportation. In this paper, we propose a method for high intensity generation of entangled photons in a two‐mode electromagnetic field. On the basis of exact solutions of the Schrödinger equation, when electrons interact in an atom with a strong two‐mode electromagnetic field, it is shown that there may be large quantum entanglement between photons. The quantum entanglement is analyzed on the basis of the Schmidt parameter. It is shown that the Schmidt parameter can reach very high values depending on the choice of characteristics of the two‐mode fields. We find the Wigner function for the considered case. Violation of Bell's inequalities for continuous variables is demonstrated.     

Electromagnetic field with induced massive term: Case with scalar field

We consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.     

Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic field

We present analytical and numerical results on the mechanism of excitation and ionization of hydrogen atoms under microwave fields. In particular we predict the existence of a critical value of the microwave field, the quantum delocalization border, above which the quantum packet delocalizes and strong excitation and ionization takes place. Below the quantum border, the packet is localized even though the corresponding classical system can be chaotic and obeys a diffusion equation.Our studies reveal some other unexpected new features of quantum dynamics which also could be observed in laboratory experiments and provides a quantum theory for subthreshold ionization.     

光线量子理论研究薄膜介质光场能量分布

因为光线量子力学方程的光线哈密顿算符不表示能量,而是具有可变折射率的物理意义,因此应用光线量子论讨论波导中光场能量分布是一个有待研究的问题.本文借鉴量子力学几率密度和几率密度矢量概念推导出光场能量分布的普遍性公式,并证明流线结构的光场中守恒定律的成立.     

Beta decay and other processes in strong electromagnetic fields

We consider effects of the fields of strong electromagnetic waves on various characteristics of quantum processes. After a qualitative discussion of the effects of external fields on the energy spectra and angular distributions of the final-state particles as well as on the total probabilities of the processes (such as decay rates and total cross sections), we present a simple method of calculating the total probabilities of processes with production of nonrelativistic charged particles. Using nuclear β decay as an example, we study the weak- and strong-field limits, as well as the field-induced β decay of nuclei stable in the absence of the external fields, both in the tunneling and multiphoton regimes. We also consider the possibility of accelerating forbidden nuclear β decays by lifting the forbiddeness due to the interaction of the parent or daughter nuclei with the field of a strong electromagnetic wave. It is shown that for currently attainable electromagnetic fields all effects on total β-decay rates are unobservably small.     

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.     

Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

Remarks on stratifying interactions in five dimensions

A geometric model is proposed in which the interaction types, namely the strong, weak, electromagnetic, and gravitational interactions, are stratified in a five-dimensional manifold. The strong and electromagnetic interactions are confined to disjoint four-spaces and the weak and gravitational interactions are proposed unified in a five-manifold bounded topologically by the strong and electromagnetic four-spaces. Further, some advantages of the five-dimensional approach to current-current interactions are discussed, and a five-dimensional approach to PCAC is presented. The model is presented in hopes of reconciling some contradictory lines of theoretical thought, and new fields for investigation are stressed.     

A Spin-Statistics Theorem for Quantum Fields¶on Curved Spacetime Manifolds¶in a Generally Covariant Framework

A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of a causal dynamical law, fixed spinor- or tensor type for all quantum fields of the theory, and that the quantum field on Minkowski spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem holds: If for some of the spacetimes the corresponding quantum field obeys the “wrong” connection between spin and statistics, then all quantum fields of the theory, on each spacetime, are trivial. Received: 1 March 2001 / Accepted: 28 May 2001