International Journal of Modern Physics A

By introducing a new Tortiose coordinate and using the notion of local equilibrium, we have studied the Hawking effect and the entropy of an arbitrarily accelerating Kerr black hole, a nonstationary black hole. The Bekenstein–Hawking entropy has been obtained by taking the same geometric cutoff relationship in the thin film model as that in the static case. Consequently, the results in the new Tortiose coordinate reveal the following two facts. First, it is correct in the opinion that the black hole entropy is determined by the horizon of a black hole, whether it is stationary or nonstationary. Second, the entropy of the nonstationary black hole shows some common essential natures with that of a static one.

An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and nonlocal families of R-matrix solutions to the modified Yang–Baxter equation. The three R-theoretic Poisson structures and the Suris quadratic bracket are derived. The resulting family of bi-Poisson structures include a seminal discrete bi-Poisson structure of Kupershmidt at a special value.

A deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply is formulated. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves to be efficient in practical computations. This technique is particularly convenient in three dimensions for Chern–Simons gauge fields, two-component fermions and four-fermion models in the large N limit, eventually coupled with quantum gravity. Differently from even dimensions, in odd dimensions it is not always possible to have propagators with fully Lorentz invariant denominators. The main features of the deformed technique are illustrated in a set of sample calculations. The regularization is universal, local, manifestly gauge-invariant and Lorentz invariant in the physical sector of space–time. In flat space power-like divergences are set to zero by default. Infinitely many evanescent operators are automatically dropped.

In addition to obtain ordinary SUSY representation related to the partner Hamiltonians, three other nonordinary SUSY representations for the quantum states of 1D Woods–Saxon and periodic Scarf potentials are obtained by the factorization methods. The ordinary SUSY representation induces laddering relations for these two models with respect to the parameters n and m that are introduced in the paper, respectively. One of the nonordinary SUSY representations involves the laddering relations of the two models with respect to the parameters m and n, respectively. Also, the other two of them induce laddering relations with respect to the parameters n and m simultaneously and inversely as well as simultaneously and agreeably.

The axion–dilaton string effective action is expressed in Einstein frame metric in a manifestly S-duality invariant form. It is shown that the moduli can be redefined to describe surface of a (2+1)-dimensional pseudosphere. The classical cosmological solutions of axion–dilaton are revisited. The Wheeler–DeWitt equation for the system is exactly solved and complete set of eigenfunctions are presented. The wave function factorizes and the one depending on the moduli is obtained by appealing to the underlying S-duality symmetry. Axion and dilaton parametrize , the S-duality group, and the Hamiltonian is expressed as a sum of the Ricci scalar and the Casimir of SU(1, 1). Therefore, the complete set of wave functions, depending on the moduli, is obtained from group theory technique. The evidence for the existence of a W-infinity algebra in axion–dilaton cosmology is presented and the origin of the algebra is primarily due to high degree of degeneracies in the wave functions. It is qualitatively argued that axion–dilaton quantum cosmology exhibits chaotic behavior in the semiclassical limit.

In this paper, we compute the general structure of two- and three-point functions in field theories that are assumed to possess an invariance under a quantum deformation of SO(4, 2). The computation is elaborated in order to fit the Hopf algebra structure.

In this paper we propose the toy model of the closed string tachyon effective action that has marginal tachyon profile as its exact solution in case of constant or linear dilaton background. Then we will apply this model for description of two-dimensional bosonic string theory. We will find that the background configuration with the spatial dependent linear dilaton, flat space–time metric and marginal tachyon profile is the exact solution of our model even if we take into account backreaction of tachyon on dilaton and on metric.

We study the spherically symmetric collapse of a fluid with nonvanishing radial pressure in higher dimensional space–time. We obtain the general exact solution in the closed form for the equation of state (P_r = γρ), which leads to the explicit construction of the root equation governing the nature (black hole versus naked singularity) of the central singularity. A remarkable feature of the root equation is its invariance for the cases; (D, γ = 0) and (D+1, γ = -1) where D is the dimension of space–time. For the ultimate end result of the collapse, these two cases are absolutely equivalent, which is indeed a very interesting new result that brings out the interplay between dimension D of space–time and the equation of state parameter γ.

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

We investigate a system of two coupled harmonic oscillators on the noncommutative plane by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle α. The obtained eigenstates as well as the eigenvalues depend on the noncommutativity parameter θ. Focusing on the ground state wave function before the transformation, we calculate the density matrix ρ₀(θ) and find that its traces Tr(ρ₀(θ)) and are not affected by the noncommutativity. Evaluating the Wigner function on confirms this. The uncertainty relation is explicitly determined and found to depend on θ. For small values of θ, the relation is shifted by a θ² term, which can be interpreted as a noncommutativity correction. The calculated entropy does not change with respect to the normal case. We consider the limits α = 0 and α = π/2. In the first case, by identifying θ to the squared magnetic length, one can recover basic features of the Hall system.