The meaning of the terms “phase” and “phase transition”

Various meanings of the terms phase and phase transition encountered in scientific literature are discussed. These terms supplement each other and cover only together all the macroscopic situations which are now denoted by this term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1988.     

The “complex trick” in five-dimensional relativity

The generation method developed by Newman et al. which creates from spherically symmetric solutions of the field equations by a complex coordinate transformation axisymmetric solutions is extended to five-dimensional relativity.     

Equivalence principle,the general theory of relativity,ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with valve properties -a one-way exchange of information—contradicts the equivalence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–15, January, 1984.     

Geometrical meaning of the Poincaré group gauge theory

We find a condition (6) under which a gauge theory of the Poincaré group is equivalent to the Einstein-Cartan theory of gravitation.     

Interrogating the Legend of Einstein's “Biggest Blunder”

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his “biggest blunder.” However, serious doubts about this reported statement have been raised in recent years. We interrogate the legend of Einstein’s “biggest blunder” statement in the context of our recent studies of Einstein’s cosmology in his later years. We find that the remark is highly compatible with Einstein’s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term as a serious error and that he very likely labelled the term his “biggest blunder” on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently discovered acceleration in cosmic expansion without the use of a cosmological constant term.     

The special theory of relativity as applied to the Born–Oppenheimer–Huang approach

In two recent publications (Int. J. Quant. Chem. 114, 1645 (2014) and Mole. Phys. 114, 227 (2016)) it was shown that the Born–Hwang (BH) treatment of a molecular system perturbed by an external field yields a set of decoupled vectorial wave equations, just like in electro-magnetism. This finding led us to declare on the existence of a new type of Fields, which were termed Molecular Fields. The fact that such fields exist implies that at the vicinity of conical intersections exist a mechanism that transforms a passing-by electric beam into a field which differs from the original electric field. This situation is reminiscent of what is encountered in astronomy where Black Holes formed by massive stars may affect the nature of a near-by beam of light. Thus, if the non-adiabatic-coupling-terms (NACT) with their singular points may affect the nature of such a beam (see the above two publications), then it would be interesting to know to what extend NACTs (and consequently also the BH equation) will be affected by the special theory of relativity as introduced by Dirac. Indeed, while applying the Dirac approach we derived the relativistic affected NACTs as well as the corresponding BH equation.     

Gödel axiom mappings in special relativity and quantum-electromagnetic theory

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (c) the unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol and are to be associated with the complex probability eⁱ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory.     

Does general relativity allow an observer to view an eternity in a finite time?

I investigate whether there are general relativistic spacetimes that allow an observerµ to collect in a finite time all the data from the worldline of another observer, where the proper length of's worldline is infinite. The existence of these spacetimes has a bearing on certain problems in computation theory. A theorem shows that most standard spacetimes cannot accommodate this scenario. There are however spacetimes which can: anti-de Sitter spacetime is one example.     

“Projective relativity” and magnetohydrodynamics

The geometrical structure of the Castelnuovo space-time and the Fantappié group are analyzed with the Inönj-Wigner method of contraction of a group with respect to the various subgroups. If we utilize the two vectorsposition andvelocity, we can study the structure of the magnetohydrodynamics tensor. It follows that from projective magnetohydrodynamics we can deduce as limiting cases four theories (two by two duals in the sense of the classical projective geometry).     

Nonperturbative calculation of the shear viscosity in hot φ4 theory in real time

Starting from the Kubo formula we calculate the shear viscosity in hot φ⁴ theory nonperturbatively by resumming ladders with a real-time version of the Bethe-Salpeter equation at finite temperature. In the weak coupling limit, the generalized Fluctuation-Dissipation Theorem is shown to decouple the Bethe-Salpeter equations for the different real-time components of the 4-point function. The resulting scalar integral equation is identical with the one obtained by Jeon using diagrammatic “cutting rules” in the Imaginary Time Formalism.     

“Conserved charges” of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory

The asymptotic symmetries in the Brans-Dicke theory are analyzed using Penrose's conformal completion method,which is independent of the coordinate system used.These symmetries,indeed,include supertranslations and Lorentz transformations for an asymptotically flat spacetime.With the Wald-Zoupas formalism,“conserved charges”and fluxes of the Bondi-Metzner-Sachs algebra are computed.The scalar degree of freedom contributes only to the Lorentz boost charge,even though it plays a role in various fluxes.The flux-balance laws are further applied to constrain the displacement memory,spin memory,and center-of-mass memory effects.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

To the theory of isotope effect in the thermodynamics of “Classical” crystals

Based on general expressions for quantum contributions to the free energy of a statistical system, an approach is developed making it possible to carry out a complete theoretical analysis of the equilibrium thermodynamic characteristics of argon-type crystals as a function of the isotopic mass. The theory is based on independently calculated (in fact, without fitting parameters) one-particle and two-particle distribution functions of the classical crystal and permits one to quantitatively describe the data on the lattice parameters of isotope crystals obtained from numerical experiments. It is pointed out that real experiments are needed to study the isotope effect in crystals of noble gases, especially in view of the fact that, according to the literature data, xenon undergoes an fcc-hcp phase transition under increased pressure.     

“Harmonic” solutions of Einstein's equations

For the example of a static spherically symmetric gravitational field with Galilean metric at infinity, it is shown that the harmonic solutions of Einstein's equations are not unique. In the whole of space, both outside and inside a spherically symmetric body in equilibrium, one can introduce a one-parameter family of harmonic coordinates corresponding to these solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 82–87, November, 1976.I thank Yu. L. Gazaryan and I. D. Novikov for a helpful discussion of the questions touched on in this note.     

Hydrogen in semiconductors: The roles of μSR and theory

Hydrogen is an unavoidable impurity in all semiconductors. It interacts with intrinsic defects (from monovacancies to dislocations), with impurities (shallow dopants, deep centers, even electrically inactive impurities), with the crystal, and with otherH interstitials. These interactions profoundly affect the electrical and optical properties of the host. Conventional experimental techniques used to study the properties of hydrogen (EPR, IR or Raman spectroscopy, etc.) have provided information on a number ofH-related defects. Theory has played a major role in these studies, not only by confirming the models proposed on the basis of experimental data, but often by explaining the data altogether or predicting new features. So far,SR has provided fundamental information on isolated hydrogen-like species in many semiconductors. It would be wonderful if thespectroscopic signature of muonium-impurity pairs could be identified or ifquantitative information regarding the stability of the various charge states of muonium could be obtained.     

Cosmic ray “knee” in the spectrum and proton-proton cross section from the point of view of new quarks

A possible explanation of the “knee” in the cosmic ray spectrum by the change in hadron-hadron interactions at the corresponding energy is discussed. It is shown that, at c.m. energies above 5 TeV, the total proton-proton cross sections obtained from cosmic ray experiments exceed the asymptotic fit made over the collider data. Such a rise of the cross sections favors the hypothesis about new chromodynamically charged degrees of freedom, the threshold of their creation being about \(\sqrt {^\mathcal{S} knee} \approx 2.3 TeV\). The properties of these new particles which are needed are discussed.