Causality, Lorentz invariance and i) the electromagnetic interaction of a massive spin-one vector field with arbitrary magnetic-dipole moment, ii) the massive Yang-Mills field

Abstract

In recent years, following the methods first used by VwLo and ZWANZmER (1), several authors have studied the causal na ture of the propagat ion of higher-spin classical fields in external potentials (3). By a consideration of several examples involving a massive spin-one vector field, the author has lent force to the conjecture that , for a field in an external potential , the classical theory is causal (in the sense of VELo and ZWA~ZlGER) if and only if the corresponding quantum theory is Lorentz invar iant (in the sense tha t there exists an operator ordering in terms of which the per turba t ion expansion for the S-operator is normal-independent) (3). I t is of interest to see if the results of ref. (3) can be extended to include interactions between classical fields, and the corresponding fully quantized theories. As a first step in this direction, two theories, whose Lorentz invariance propert ies at the fully quantized level are well known, are here considered at the classical level. The first theory to be discussed is the electromagnetic interact ion of a massive spinone vector field with a rb i t ra ry magnetic-dipole moment. This theory was found b y L ~ and YA~G to be noncovariant a t the fully quantized level (4). Later , NAKAI~UEA (6) and Tzou (e) demonstra ted that , by the inclusion of an appropria te fourth-degree selfinteract ion of the vector field into the Lee-Yang theory, a Lorentzinvar iant theory results. Since i t is the magnetic-dipole interaction, and not the minimal electromagnetic interaction, which gives rise to the covariance difficulties, the la t te r will, for caleulat ional and notat ional simplicity, be omit ted from the following discussion. Thus the