Nonrenormalizability of super Φ3 theory for the N=2 vector gauge supermultiplet

The super ³ theory in N=2 superspace is considered for the N=2 vector gauge supermultiplet. Its nonrenormalizability is demonstrated at the one loop level by using supergraph techniques.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 100–103, August, 1985.In conclusion the author is thankful to I. V. Tyutin for useful discussions.     

A note on the ‘one-link’ integral of U(N) lattice gauge theory

We calculate the one-link U(N) integral in closed form by a direct method, i.e., polar decomposition and integration over agular variables. The result agrees with the known solution of the Brower-Nauenberg equation, at least forN4.Notice that in Reference [7] a direct integration was given forN=2 andN=3 However, the identification with Equation (2) was not given explicity, but on the basis on the assumed uniqueness of the solution.     

Solutions of D. A. Raikov’s problems in the theory of topological vector spaces

The solutions and the role of problems posed by D. A. Raikov in the sixties are discussed.     

Concavity of the QQ̄ potential in N=4 super Yang-Mills gauge theory and AdS/CFT duality

We derive a generalised concavity condition for potentials between static sources obtained from Wilson loops coupling both to gauge bosons and a set of scalar fields. It involves the second derivatives with respect to the distance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretical condition as a nontrivial consistency check of the AdS/CFT duality.     

Thermodynamic theory of the Tolman’s length

There still exists controversy on the sign and magnitude of the Tolman’s length and the Tolman’s gap.Further experimental,computational and theoretical investigations on them are needed to solve this problem.In 2006,Blokhuis and Kuipers obtained a rigorous relationship between the Tolman’s length and other thermodynamic quantities for the single-component liquid-vapour system.In the present paper,we derive two general relationships between the Tolman’s length and other thermodynamic quantities for the single-component liquid-vapour system.The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.     

Duality in Yang’s theory of gravity

The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a vacuum degeneracy. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.     

On Δβ and the search for asymptotic scaling in lattice gauge theory

An ansatz for the β-function of SU(3) lattice gauge theory in four dimensions whose parameters are determined by Monte Carlo data is used both to compare different sets of data for Δβ and to study systematic errors. The data for Δβ obtained from different values of the block-spin renormalization group scaling factor are shown to be compatible within statistical errors. However the data is easily consistent with sizeable deviations (ca. 30% or more) from the two-loop approximation to the renormalization group scaling formula for physical quantities in the region of coupling for which Δβ essentially takes on its asymptotic value.     

Maslov’s asymptotic methods in problems of the theory of optical lattices

Application of Maslov’s asymptotic methods to equations that arise in the theory of optical lattices was considered. The occurrence of a small parameter in the Schrödinger equations with potentials of three-dimensional and controlled optical lattice was investigated and the conditions of application of Maslov’s asymptotic methods for solving these equations was determined. Consideration of different conditions imposed on the parameters in these potentials led to the use of two different methods for solving the arising equations: Maslov’s method of a complex germ and Maslov’s operator-valued method of a complex germ. Expressions that can be used to calculate the desired characteristics of the atomic systems under consideration in optical lattices were derived.     

How does the s(E + N) equation work? Comparisons with a modified Swain–Scott equation (E + sN) and revision of the N1 scale of solvent nucleophilicity

Modifications of the Swain–Scott equation (log k/k₀) = sn) give an equation log k₁ = (E + sN₁′); k₁ is the rate constant, E is an electrophilicity parameter, N₁′ is a solvent nucleophilicity parameter and s is an electrophile‐specific sensitivity parameter. The equation is tested using over 300 published first‐order rate constants (k₁) for decay of a range of benzhydrylium cations in various solvents, on which the published N₁ scale of solvent nucleophilicity is based (S. Minegishi, S. Kobayashi and H. Mayr, J. Am. Chem. Soc. 2004, 126, 5174–5181) using the alternative equation log k = s(E + N₁), in which s is a nucleophile‐specific parameter. The modified (E + sN₁′) equation provides a revised N₁′ scale of solvent nucleophilicity, and a more precise fit, with less than half the number of adjustable parameters. It is found that the sensitivities of the benzhydrylium cations to changes in solvent nucleophilicity decrease slightly as reactivity increases, in contrast to s(E + N) equations, which show no trends in s values. It is proposed that more reliable N scales can be defined using (E + sN), because N is determined directly from definitions, and residual errors (e.g. experimental or due to solvation effects) can be incorporated into the slope and intercept. The complex reasons for the success of equations of the type log k = s(E + N) are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

A magnetic-monopole-type solution in the Poincaré gauge field theory of gravity

In a microscopical theory of gravity the coupling of internal gauge degrees of freedom to those of space-time are studied. A magnetic-monopole-type solution for the coupledSO(3) Yang-Mills-Higgs system in a space-time with curvature and torsion is derived. The coupling constant of the Lorentz gauge bosons can be related directly to the (constant) Higgs field and to the cosmological constant which is induced by the quadratic curvature terms in the Lagrangian. This reveals a new interpretation of the parameters entering the general Lagrangian density of the Poincaré gauge field theory (PG).     

Center vortex properties in the Laplace-center gauge of SU(2) Yang–Mills theory

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.     

Exotic fermions in Kadyshevsky’s theory and the possibility to detect them

As it is known, the principal research interest of V.G. Kadyshevsky was the development of a geometric approach to quantum field theory with a constraint imposed on the mass spectrum of elementary particles. Non-Hermitian operators arising in this case seemed to be a major obstacle to the development of a consistent theory. These issues have been resolved recently, and the introduction of the pseudo-Hermitian algebraic approach to the construction of quantum theory was a major advance in this physical research. The central point of such theories is the construction of PT-symmetric non-Hermitian Hamiltonians with real eigenvalues. It is important to note that both purely theoretical and experimental studies (e.g., in non-Hermitian optics) are found among the many published papers on this subject. Therefore, we believe that the development of pseudo-Hermitian relativistic quantum theory with a maximal mass may provide favorable opportunities to discuss the possible experimental verification of theoretical results obtained in this field. Kadyshevsky himself regarded the hypothesis of existence of new particles, which he called exotic fermions, as an important prediction of his theory. The possibility of discovery of exotic neutrinos in precision experiments on the determination of the neutrino mass is discussed in the present study.     

On study of the theory and algorithm of the three dimensional coupled mode-parabolic equation

A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes     

Nordström’s scalar theory of gravity and the equivalence principle

General Relativity obeys the three equivalence principles, the “weak” one (all test bodies fall the same way in a given gravitational field), the “Einstein” one (gravity is locally effaced in a freely falling reference frame) and the “strong” one (the gravitational mass of a system equals its inertial mass to which all forms of energy, including gravitational energy, contribute). The first principle holds because matter is minimally coupled to the metric of a curved spacetime so that test bodies follow geodesics. The second holds because Minkowskian coordinates can be used in the vicinity of any event. The fact that the latter, strong, principle holds is ultimately due to the existence of superpotentials which allow to define the inertial mass of a gravitating system by means of its asymptotic gravitational field, that is, in terms of its gravitational mass. Nordström’s theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a “Nordström-Katz” superpotential.