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Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups I

In a previous paper, we showed how wavefunctions which transform in a relativistic manner in configuration space can be expanded in terms of amplitudes, which for nonzero mass transform like the wavefunctions for irreducible representations of the proper, orthochronous, inhomogeneous Lorentz group. A simple algorithm was given to obtain the expansion. In the present paper, we extend the results to include zero‐mass amplitudes. It is shown that for wavefunctions which are required to transform under the homogeneous Lorentz group such that the matrices which involve the spinor indices are finite dimensional, the zero‐mass amplitudes transform under nonunitary representations of the inhomogeneous Lorentz group. However, it is possible to split up each such nonunitary representation into a part which corresponds to a unitary representation for finite spin and into a part which corresponds to an unphysical change of wavefunction. As examples of the technique, we consider wavefunctions which transform as an ant...

Reduction of Relativistic Wavefunctions to the Irreducible Representations of the Inhomogeneous Lorentz Group. Part II. Zero‐Mass Components

The formal structure and the free‐particle solutions of the field equations (Sμνpν + mγμ)ψ = pμψ, derived recently by the author [Nuovo Cimento 51A, 864 (1967)] for realizations of the inhomogeneous de Sitter group are discussed. The enveloping algebra of the group is developed, and the covariance of the field equations under the five‐dimensional rotations C, P, and T is proved. Bhabha's representation of the matrices γμ is completed. Observables, expectation, values and the scalar product are defined, and classical conservation laws are derived. The field equations are derived from a variational principle for the usual Lagrangian density ψ(−iγμ∂μ+m)ψ under a certain restriction. The free‐particle solutions of the field equations are obtained in the canonical and the extreme relativistic representations. The connections between the wavefunctions in these representations, and also in the Foldy‐Wouthuysen representation, are derived.

De Sitter Symmetric Field Theory. I. One‐Particle Theory

Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species $A$ and $B$ for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek(DLVO)) pair potential but the $AB$ cross-interaction is different from the geometric mean of the two direct $AA$ and $BB$ interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then getting significantly negative and is getting then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO-theory.

Nonadditivity in the effective interactions of binary charged colloidal suspensions

We study the covariant quantization of the electromagnetic field by means of a 4-vector potential, starting from the general results of Wigner on Poincare invariance. From this sole hypothesis, we deduce that such a quantization may only be performed using indefinite metrics and requiring the Lorentz condition (in the form given by Gupta and Bleuler) together with gauge invariance. Moreover, we exhibit all the possible indefinite metrics: they form a two-parameter family which of course includes Gupta-Bleuler’s metric and they all lead to the same physically significant results.

Poincaré covariance and quantization of zero-mass fields

Covariant wave equations for massless particles

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Covariant wave equations for massless particles