The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ  , the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0$\kappa \ne 0$ one clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.     

Complexification of gauge theories

For the case of a first-class constrained system with equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations G is equivalent to the single process of dividing out the initial phase space by the complexification G_C of G. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold for the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.     

The off-mass shell physical state projection operator for the dual resonance model

Extending recent work of Brink and Olive, an off-mass shell physical state projection operator for the critical dimension, d = 26, of space-time, for the conventional dual resonance model is constructed. It can be used to give a direct calculation of the single planar dual loop amplitude, and to express amplitudes entirely in terms of physical state creation operators.     

Physics in multidimensional spaces and the beginning of metagalaxy

Physical phenomena in the Riemannian space of arbitrary dimensionality D = D′ + 1 (D′ = integer) are analyzed. It is noted, that with the dimensionality of physical space of the observable Metagalaxy D = 3 +1 very important physical features are connected, which distinguish that value of D from the others. However, this does not mean that the dimensionality of the physical space of the whole Universe must coincide with the value D = 3 + 1. This conclusion is confirmed by the geometric interpretation of supergravity and Kaluza-Klein theory. Different models of compactification and dimensional reduction of physical space and models of Metagalaxy formation in multidimentional spaces are reviewed.     

A generalized Slavnov-invariant Abelian Higgs-Kibble model

The supersymmetric structure of the Becchi-Rouet-Stora invariance is used for investigating the Abelian Higgs-Kibble model. It allows for a symmetric photon mass M, in which case a massless scalar state corresponding to the Goldstone model belongs to the physical sector. If M = 0, i.e. the photon mass is generated by the Higgs mechanism, this state is decoupled from the physical sector, as usual. The BPHZ renormalization procedure is used.     

Generalized Heisenberg algebra and algebraic method: The example of an infinite square-well potential

We discuss the role of generalized Heisenberg algebras (GHA) in obtaining an algebraic method to describe physical systems. The method consists in finding the GHA associated to a physical system and the relations between its generators and the physical observables. We choose as an example the infinite square-well potential for which we discuss the representations of the corresponding GHA. We suggest a way of constructing a physical realization of the generators of some GHA and apply it to the square-well potential. An expression for the position operator x in terms of the generators of the algebra is given and we compute its matrix elements.     

Binding in velocity dependent potentials and pion-nuclear systems

Properties of bound states in velocity-dependent potentials are discussed and the WKB approximation is established and used to derive quantization conditions for such states. The most updated zero-range optical potential for pionic atoms is reviewed and employed for the calculation of strongly bound π^? nuclear states. Some of the several physical mechanisms, in particular the πN finite interaction range, which affect the whole issue of binding and critically determine the number of bound states expected, are qualitatively discussed. Unless dynamical suppression of π^? nuclear absorption occurs below threshold, the calculated states are too wide to be considered as well-defined physical states.     

Light-scattering experiments in dye-doped liquid crystals both to determine crystal parameters and to construct consistent neural network empirical physical formulas for scattering amplitudes

The aim of this paper is two-fold. Firstly, static laser light-scattering amplitude measurements in azo-dye doped nematic liquid crystals (NLCs) were made versus scattering angle, temperature and applied bias voltage. Three NLC parameters were determined: the elastic constant ratios K₁₁/K₂₂ by regression, phase transition temperatures, and Freedericksz voltages from the graphs. They were all doping ratio dependent. Secondly, as a novel approach, by a nonlinear universal function approximator layered feedforward neural network (LFNN) we constructed an explicit form of empirical physical formulas (EPFs) for theoretically unknown nonlinear azo-dye doped NLC scattering amplitude functions. Excellent LFNN test set (i.e. yet-to-be measured experimental data) predictions prove that the constructed LFNN-EPPs estimate unknown amplitude functions consistently. The LFFN-EPFs, too, confirmed the doping-ratio dependency. Also, comparing LFNN and regression amplitude fits, the LFNN fits were significantly better. In conclusion, physical laws embedded in the physical data can be consistently extracted by LFNN. One major potential application in the nonlinear optics domain is that these LFNN-EPFs, by differentiation, integration, minimization, etc., can be used to obtain further NLC scattering amplitude related molecular structural physical quantities. This could in turn help us to develop new nonlinear optical materials.     

The coherent state variational algorithm: A numerical method for solving large-N gauge theories

This paper presents a new approach for studying large-N gauge theories which directly exploits the classical nature of the N → ∞ limit. This method supplies a practical algorithm for computing and minimizing the classical hamiltonian (or effective action) which governs N = ∞ dynamics, and allows one to calculate physical quantities such as the mass spectrum or scattering amplitudes of glueballs or mesons. Two different implementations of the basic ideas are discussed; one variant provides an algorithm for constructing N = ∞ master field matrices, while the other works directly with a list of expectation values of physical operators. Algorithms are developed for both the hamiltonian and euclidean formulations of lattice gauge theories. The inclusion of fermions in the hamiltonian version is also described. Detailed tests of the method in the context of the exactly solvable one-plaquette model are presented.     

The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.     

RLC electrical circuit of non-integer order

In this work a fractional differential equation for the electrical RLC circuit is studied. The order of the derivative being considered is 0 < γ ≤ 1. To keep the dimensionality of the physical quantities R, L and C an auxiliary parameter γ is introduced. This parameter characterizes the existence of fractional components in the system. It is shown that there is a relation between and σ through the physical parameters RLC of the circuit. Due to this relation, the analytical solution is given in terms of the Mittag-Leffler function depending on the order of the fractional differential equation.     

Jeans' gravitational instability of a thermally conducting plasma

The gravitational instability of an infinitely extending homogenous plasma endowed with several physical mechanisms, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity is considered. The main result is that the various parameters play different physical roles in the perturbed problem. Jeans' criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q=1, q being the nonextensive parameter.     

The elusive quantal individual

In the formal hedgehog representation of quantum mechanics [5] (ambiguous) weights are derived for hedgehogs with a finite number of questions and answers, in particular applied to spin $\text{1}\text{2}$ and to correlated spin $\text{1}\text{2}$ pairs. Unavoidable negative weights are a clear signal for conceptual difficulties in quantum mechanical interpretation. If these weights had been presupposed to be non-negative, they could have led to Bell-like inequalities inconsistent with quantum mechanics. This is what has happened already in various special models.Owing to the indefinite weights, the hedgehog hypothesis of one-to-one mapping between individual physical samples and individual fictitious hedgehogs cannot be maintained. If no physical interpretation is conceived for the negative weights, the only way to avoid unsolved conceptual difficulties appears to resign (even in the hedgehog representation) to the skeptical ensemble interpretation [1], without theorizing about individual physical samples at all.     

Effect of long-term physical aging on the kinetic parameters in a common pharmaceutical drug: Flutab

Differential scanning calorimetry (DSC) measurements were performed to investigate the effects of long-term physical aging on kinetic parameters of the pharmaceutical drug (Flutab^®). Kinetics parameters such as activation energy (E) and fragility parameter (m) of the glass transition for aged and rejuvenated glasses were determined using different kinetic models. Evidence of variation of E with temperature is presented. It is shown in this work that natural storage of the drug introduced significant physical aging as indicated by changes in the glass transition temperature, activation energy and fragility parameter.     

Reduced Dirac-Kähler lattice fermion action

It is shown that the lattice Dirac-Kähler action is reducible under a chiral-like transformation. This provides a new lattice fermion action for spinors that have 2^d−1 components (instead of 2^d), with the property that, in the free case, each component satisfies the lattice euclidean Klein-Gordon equation. Reflection positivity is satisfied on the lattice, thus assuring a (positive) physical Hilbert space. In d = 4 dimensions the spinors have 8 components, and the correct physical chiral anomaly in the continuum limit. The action is suitable for QCD quarks which, in the continuum limit, are described by Dirac spinors that occur in flavor doublets.     

Construction of physical states in Yang-Mills theory: The time-like gauge

We construct physical states in pure Yang-Mills theory in the time-like gauge A_α⁰ = 0. We also construct a complete basis in the physical subspace of Hilbert space. Comparison is made with a recent paper by Eylon.     

Relativistic interactions for meson-nucleon systems in the clothed particle representation

The method of unitary clothing transformations (see [1–3] and references therein) enables one to represent the initial Hamiltonian H for interacting fields in terms of the creation (destruction) operators for the so-called clothed (physical) particles and their relativistic interactions. Using this clothed particle representation (CPR) of H and starting from the Yukawa-type couplings between fermions (nucleons and antinucleons) and bosons (π-, η-, ρ-, ω-mesons, etc.), we have derived a new family of the Hermitian and energy-independent interactions for physical processes πN → πN, NN → NN, NN ? πNN and NNN → NNN. Each of the obtained analytic expressions in momentum space is the sum of a Feynman-like part and some off-energy-shell correction term. The latter cannot appear when calculating the corresponding S-matrix elements by Feynman rules.     

Comment on “propagation of ultrashort light pulses in a resonant medium”

Previous conclusions on the propagation of ultrashort light pulses in a resonant medium are found to be in error. There is no physical basis for rejecting the nd u and dn u solutions.     

Anisotropy of the work function change in physical adsorption

Smoluchowski's concept of the surface double layer of bare metals is extended for physical adsorption of rare gas atoms on metal surfaces. With the use of the polarization approach it is possible to show that the work function decrease on physical adsorption of rare gases is anisotropic. A simple rule is suggested according to which the work function change produced by physical adsorption of the given rare gas on different crystal faces of the same metal [-Δφ(hkl)] decreases with increasing work function of the bare face [φ₀(hkl)] and/or with increasing packing density of the bare face. The former correlation is quantitative, whereas the latter correlation is only qualitative. The above predictions are compared with the first data available in the literature.     

CP violation in vector-like theories of weak interaction

In vector-like theories of weak interaction where CP is broken spontaneously through the vacuum, one can always find a proper CP transformation law for the physical particles that violates CP only in the Higgs sector, but not in the fermion gauge coupling.