On the vectorial fields with position-independent stochastic behavior

Vectorial fields with position-independent stochastic behavior within a certain region are analyzed. More specifically, we deal with the transverse components of this class of beamlike fields (the longitudinal component assumed to be negligible). The general form of the cross-spectral density tensor (CDT) of these fields is shown. Attention is also focused on the properties of these kinds of fields. Thus, among other characteristics, it is seen that the CDT of these fields can be written as the sum of two CDTs associated, respectively, to a totally polarized field and to an unpolarized field. It is also shown that, for such fields, a Young's interference experiment can always be performed whose fringe visibility is optimized. This behavior has analytically been characterized by means of a certain parameter, valid for general beamlike fields. It is shown that, for the fields studied, this parameter reaches its maximum value.     

Measurement-induced-nonlocality via the Unruh effect

Treated beyond the single-mode approximation, Measurement-Induced-Nonlocality (MIN) is investigated for both Dirac and Bosonic fields in non-inertial frames. Two distinct differences between the Dirac and Bosonic fields are: (i) the MIN for Dirac fields persists for any acceleration, while the quantity for Bosonic fields does decay to zero in the infinite acceleration limit; (ii) the dynamic behaviors of the MIN for Dirac fields is quite different from the Bosonic fields case. Besides, we also study the nonlocality for Dirac fields and find that the MIN is more general than the quantum nonlocality related to violation of Bell’s inequalities. Meanwhile some discussions of geometric discord are presented too.     

Fields with vanishing colour-currents

We consider spinor, scalar and vector fields with colour degrees of freedom and find the classical solutions when the constraint of vanishing colour currents is imposed. We find that there are no non-trivialc-number solutions for spinor fields transforming as a triplet under SU(3), although solutions exist for scalar and vector fields. We also show that the colour current of spinor fields coupled to an instanton is zero.     

Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.     

Quantum field theory of fermions constructed from bosons. Generalization to Para-Fermi statistics

It is proved that Fermi fields can, in principle, be constructed in terms of Bose fields, without losing any of the physical properties of the Fermi fields such as, for example, Pauli's Principle. As an example, a Fermi field satisfying Dirac's equation is constructed in terms of Bose fields. Para-Fermi fields are constructed as well. Consequences: Physical theories can, in principle, be reformulated in such a way that Fermions and para-Fermions are described in terms of Bosons.     

Generation of perturbations by means of decoupled equations and their adjoints

It is shown that the procedure introduced by Wald for constructing solutions of a coupled system of linear partial differential equations from the solution of a single equation, based on the concept of the adjoint of a linear partial differential operator, can be extended to equations involving spinor fields, matrix fields and two or more fields. Some results concerning massless spinor fields are presented and the application of the method to linear perturbations of Yang-Mills fields and of Einstein-Maxwell fields is indicated.     

Massless Fields as Unitary Representations of the Poincaré Group

Relativistic zero-mass fields are described as manifestly covariant unitary irreducible representations of the Poincaré group. The wave-equations, which are a necessary condition for unitarity, are constructed for spinor fields of arbitrary spin and for tensor fields of integer spin. Poincaré covariance together with causality and positive energy are used to determine the commutators of quantized fields up to a positive multiple and to prove the spin-statistics theorem. The use of potentials for boson fields is discussed and it is shown that, at the expense of manifest covariance, potentials may be introduced as zero-mass limits of the massive Wigner representations.     

Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function

A simple formalism relating image fields to object fields, similar to that of the scalar and paraxial case, is presented for an aplanatic system obeying the sine condition, which shows that the vector plane-wave spectrum of image fields is equal to the product of the vector coherent transfer function due to the x- and y-polarized point electric field source and the scalar spectrum of the corresponding transverse object fields. Utilizing this formula and dyadic Green's function, a rigorous imaging theory of an aplanatic system for the point electric current source through a stratified medium is readily developed.     

Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is reviewed. Subsequently, the entire set of field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in effect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.     

Degree of polarization in near fields of thermal sources: effects of surface waves

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the 3 x 3 coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.     

Entropy of generalized Gaussian optical fields

We consider two definitions of entropy: thermodynamic entropy and signal entropy. We compare their value for the class of generalized Gaussian fields. The first definition is well adapted to monomode stationary fields, while the second one is bounded only for multimode fields. We prove that these two notions are definitely different, for example, the real Gaussian field has a maximum signal entropy and a minimum thermodynamic entropy (among the Gaussian fields).     

Beta functions and S-matrix in string theory

The relationship between sigma model β-functions and string theory scattering amplitudes is proved. We derive our results for the closed bosonic string using the weak field expansion around the flat space. The equations of motion for all the background fields, including the heavy fields are considered. We show that the effective equations for the light fields are obtained by integrating out the heavy fields. It is shown that the contributions to the β-functions come from the boundary of moduli space on a punctured Riemann surface. String loop corrections to the equations of motion are also studied.     

Singularities in speckled speckle

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 10(4) for experimentally realistic source parameters.     

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrödinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.     

Moving average fields, macro-scale response measures, and homogenizing micro-scale variation

There are two critical issues when deriving a macro-scale prediction model starting from a more complete, underlying model. The first is the precise relationship of the fields predicted by the more complete model and the fields predicted by the macro-scale model. The second is the manner of solving a closure problem that is invariably encountered in all such derivations. The understanding that moving averages of the fields predicted by the more complete model are the fields predicted by the macro-scale model is challenged on the grounds that accomplishing a moving average does not eliminate micro-scale variation, it only appears to do so in one representation of the moving average field. The solution of a closure problem by assumption is challenged on the grounds that the most common assumptions are demonstrably invalid, even while leading to prediction models that can provide reasonable estimates of the macro-scale response in some scenarios. In presenting the challenges, it is further shown how a multiresolution analysis by an orthogonal wavelet system provides a framework for both precisely defining macro-scale response fields, i.e., fields from which all micro-scale variation has been eliminated, and presenting a formally exact solution for a precisely described closure problem.     

Prime field decompositions and infinitely divisible states on Borchers' tensor algebra

We generalize some notions of probability theory and theory of group representations to field theory and to states on the Borchers algebraS. It is shown that every field (relativistic and Euclidean, ...) can be decomposed into a countable number of prime fields and an infinitely divisible field. In terms of states this means that every state onS is a product of an infinitely divisible state and a countable number of prime states, and in this formulation it applies equally well to correlation functions of statistical mechanics and to moments of linear stochastic processes overS orD. Necessary and sufficient conditions for infinitely divisible states are given. It is shown that the fields of the ø ₂ ⁴ -theory are either prime or contain prime factors. Our results reduce the classification problem of Wightman and Euclidean fields to that of prime fields and infinitely divisible fields. It is pointed out that prime fields are relevant for a nontrivial scattering theory.     

Quantization of bag-like solitons

The method of collective coordinates is used to quantize bag-like solitons formed by scalar and spinor fields. This method leads to approximate wave functions for quarks in the bag that are and spinor fields. This method leads to approximate wave functions for quarks in the bag that are orthogonal to the translation modes. Solutions are given for the MIT bag limit of the fields.     

Polychromatic polarization singularities

Elliptical polarization can appear in only monochromatic optical fields. In polychromatic vector fields the polarization is a Lissajous figure, but in only commensurate fields do the figures have well-defined shapes; in other fields the shapes are undefined. Nonetheless, I show that a given paraxial polychromatic vector field has a coherency ellipse field associated with it that contains polarization singularities and stationary points that are surrogates for the corresponding critical points of the parent optical field.     

Interaction between gravity and moving superconductors

We propose a unified phenomenological theory to investigate the interaction between arbitrarily moving superconductors and gravitational fields including the Newtonian gravity, gravitational waves, vector transverse gravitoelectric fields, and vector gravitomagnetic fields. In the limit of weak field and low velocity, the expressions for the induced electromagnetic and gravitational fields in the interior of a moving superconductor are obtained. The Meissner effect, London moment, DeWitt effect, effects of gravitational wave on a superconductor, and induced electric fields in the interior of a freely vibrating superconductor are recovered from these two expressions. We demonstrate that the weak equivalence principle is valid in superconductivity, that Newtonian gravity and gravitational waves will penetrate either a moving superconductor or a superconductor at rest, and that a superconductor at rest cannot shield either vector gravitomagnetic fields or vector transverse gravitoelectric fields.