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This paper is the second of a set of two papers on curvature collineations in general relativity. The first paper presented the mathematical basis of curvature collineations and a possible approach to their study. This paper continues from the first one by investigating in detail many of the...
An explicit expression for the Wigner coefficients coupling two positive (or negative) discrete series of the representations is obtained and the Racah coefficients for these cases are found with a single sum.
Arnold’s miniversal deformations of the matrix canonical forms for the traceless Ricci tensor C are found. The diagram presenting all possible degenerations for the algebraic types of C is given.
It is obtained, in four‐dimensional de Sitter and anti‐de Sitter spaces, the two‐point functions of the quantum p ‐forms corresponding to maximally symmetric and Hadamard vacua. It is then determined the associated renormalized stress‐energy tensors.
After an introductory mathematical review of the general concept of self‐similarity with respect to a given rescaling algebra, attention is focused on the case of Newtonian systems in Galilean space‐time, whose self‐similarity transformations will form subgroups of the maximal...
It is developed, in a curved four‐dimensional space‐time, the quantum field theory of p ‐forms. In particular, from the Ward–Lichnerowicz identity a 1 ... a p b 1 ′ ... b p ′ ; a p + a 1 ... a p −1 b 1 ′ ... b p −1 ; b p ′ = 0 G ( p ) a 1 . . . a p b 1 ′ . . . b p ′ ; a p...
The existence of Lie‐point symmetries for a family of partial differential equations (PDEs) written in Hirota’s bilinear formalism is investigated. These equations have been studied in previous publications from the point of view of the existence of multisoliton solutions and also of the...
Open Robertson–Walker cosmologies of multiple spatial connectivity provide a challenging example for the possible influence of the global topological structure of space‐time on the laws of microscopic motion. Free geodesic motion is investigated in such cosmologies in the context of first...
It is shown that the compact lattice scalar field theory converges in the sense of the correlation functions to its continuum limit when simultaneously the lattice spacing tends to zero and the amplitude cutoff and the lattice volume go to infinity. This is achieved in any number of dimensions...
The nilpotent quantity that is invariant under the N =2 superprojective transformations is constructed. Also commented on is the parametrization of such transformations.
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