International Journal of Modern Physics A

Momentum-subtraction techniques, specifically BPHZ and Zimmermann’s Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

Two classical models for particles with internal structure and which describe Regge trajectories are developed. The remarkable geometric and other properties of the two internal spaces are highlighted. It is shown that the conditions of positive time-like four-velocity and energy momentum for the classical system imply strong and physically reasonable conditions on the Regge mass-spin relationship.

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

A 3×3 matrix formalism for the E₆ group is used to identify the generators of E₆ with the extra U(1) low energy gauge groups considered in the context of superstring theories. The couplings between the gauge bosons, the fermions and the 27-Higgs field are discussed and a brief review of phenomenological results are given.

We develop a covariant canonical formalism for supergravity theories and consider Lagrangian densities which are polynomial in the curvatures in any space-time dimension. Our formalism is particularly suited for generic free differential algebras.

The existence of a topological double-covering for the GL(n, R) and diffeomorphism groups is proven. These groups do not have finite-dimensional faithful representations. Common mistakes in the literature are corrected. A theorem concerning an inner automorphism is proven, allowing for the construction of the corresponding infinite-component spinor fields. The effect of covariance on the Hilbert space is explained.