Modern Physics Letters A

In this letter we provide a new proof of a general theorem on gravitational lenses, first proven by Burke (1981) for the special case of thin lenses. The theorem states that a transparent gravitational lens with non-singular mass distribution produces an odd number of images of a point source. Our general proof shows that the topological degree finds natural and interesting applications in the theory of gravitational lenses.

In the previous paper, it has been pointed out that, for any model with real bound state in relativistic quantum field theory, Feynman rules do not give the physical amplitude in which the effects of real bound state are considered. By investigating this fact, it is found that an important guiding principle indispensable to discuss real bound state problems is unknown. The way to investigate this principle is not within the framework of relativistic quantum field theory.

Two explicit q-deformations each of SU(2) and SU(1,1) algebras are constructed by simply imposing the condition of obtaining the limiting classical algebras. No explicit transformations of the generators are used. One construction results in the standard SU_q(2) and SU_q(1,1) algebras with q-deforming functionals as infinite odd power series of both J₃ and the deformation parameter q. The other construction (also with q-deforming functionals as infinite power series) seems to be new, with additional free parameters in both the algebras and Casimirs.

We compute the one-loop effective action and the conformal anomaly associated with the product ⊗_pℒ_p of the Laplace type operators ℒ_p, p=1,2, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.

We study the possibility that the dilaton plays the role of the dark matter of the universe. We find that the condition for the dilaton to be the dark matter of the universe strongly restricts its mass to be around 0.5 keV or 270 MeV. For the other mass ranges, the dilaton either undercloses or overcloses the universe. The 0.5 keV dilaton has the free-streaming distance of about 1.4 Mpc and becomes and excellent candidate of a warm dark matter, while the 270 MeV one has the free-streaming distance of about 7.4 pc and becomes a cold dark matter. We discuss the possible ways to detect the dilaton experimentally.

We point out an important role of conformal invariant observables in the formulation of quantum cosmology with a normalizable wave function which bears a direct relationship to the Friedmann observational evolution of the Universe (with redshift and Hubble law). Conformal invariant field variables allow us to establish relation between standard cosmological models and quantum field theory actions. The conformal symmetry principle excludes the Higgs potential from the Weinberg–Salam model and includes the Penrose–Chernikov–Tagirov term. In the conformal version of the standard model for electroweak interaction unified with the Einstein gravity, the Higgs field is absorbed by the space metric so that the elementary particle masses and the evolution of the Universe have one and the same origin. In the flat-space limit we got the σ-version of the Weinberg–Salam model without the Higgs particle-like excitations.

We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.

The effective potential in the model introduced by Buchbinder–Inagaki–Odintsov (BIO)¹ which represents SUSY NJL model non-minimally coupled with the external gravitational field is found. The topology of the space is considered to be nontrivial. Chiral symmetry breaking under the action of external curvature and nontrivial topology is investigated.

Using the observation that configurations of N polymers with hard core interactions on a closed random surface correspond to random surfaces with N boundary components, we calculate the free energy of a gas of polymers interacting with fully quantized two-dimensioanal gravity. We derive the equation of state for the polymer gas and find that all the virial coefficients beyond the second one vanish identically.

We conjecture that the neutral black hole pair production is related to the vacuum fluctuation of pure gravity via the Casimir-like energy. Implications on the foam-like structure of space–time are discussed.