Modern Physics Letters A

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by P. Ramond, S.-S. Kim and myself where we describe the supergravity in the light-cone formalism. We show how the Cremmer–Julia E₇₍₇₎ nonlinear symmetry is implemented and how the full supermultiplet is a representation of the E₇₍₇₎ symmetry. I also show how the E₇₍₇₎ symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.

A five-dimensional Einstein spacetime with (non)vanishing cosmological constant is analyzed in detail. The metric is in close analogy with the four-dimensional massless uncharged C-metric in many aspects. The coordinate system, horizons and causal structures, relations to standard form of de Sitter, anti de Sitter and Minkowski vacua are investigated. After a boost and Kaluza–Klein reduction, we get an exact solution of four-dimensional Einstein–Maxwell–Liouville theory which reduces to a solution to Einstein–Liouville theory in the limit of zero boost velocity and to that of Einstein–Maxwell–dilaton theory in the case of zero cosmological constant.

Kalb–Ramond equations for massive and massless particles are considered in the framework of the Petiau–Duffin–Kemmer formalism. We obtain 10×10 matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy–momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.

We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four spacetime dimensions, and derive the (inflaton) scalar potential in the equivalent scalar–tensor gravity model. The inflaton scalar potential is used to compute the (CMB) observables of inflation, associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar–tensor gravity theories.

The fermionic one-loop vacuum energy of the superstring theory in a system of non-parallel D1-branes is derived by applying the path integral formalism.

Reparametrization invariant dynamics on a sphere, being parametrized by angular momentum coordinates, represents an appropriate framework for semiclassical description of nonrelativistic spin. The space can be quantized according to Berezin–Marinov prescription, replacing the coordinates by Pauli matrices. Following the scheme, we present two semiclassical models for describing spin without the use of Grassmann variables. The first model implies Pauli equation upon the canonical quantization. The second model produces nonrelativistic limit of the Dirac equation implying correct value for the electron spin magnetic moment.

Laws of thermodynamics have been examined for the universe filled with a perfect fluid, obeying an adiabatic equation of state p = γρ-A/ρ^α (called modified Chaplygin gas), where γ, A and α are positive constants and ρ and p are energy density and thermodynamic pressure respectively. Using general thermodynamics, the behavior of temperature and the thermodynamic stability has been discussed for modified Chaplygin gas. A scenario is obtained such that the thermal equation of state depends on both temperature and volume and there will be thermodynamic stability during the expansion process so that the fluid cools down through the expansion without any phase transition (or passing through any critical point).