Comments on Quantum Field Theory of Tachyons

Abstract

The problem of tachyons is investigated within the framework of quantum field theory. The quantization methods for a free scalar tachyon field, which have so far been proposed by various authors, are critically reviewed. Among them the Arons-Sudarshan method is found to be most satisfactory, which guarantees at least the relativistic covariance of the theory at the expense of locality and reasonable energy spectrum. On the basis of this method, interactions of a tachyon field are investigated. It is found that causal S-matrices do not exist as far as interaction terms are restricted to the ordinary, local-polynomial type. A model S-matrix, which is unitary but not causal, is then assumed, and the reinterpretation principle is applied to it in order to remove states of negative-energy tachyons. It is found that the reinterpreted S-matrix thus obtained is not consistent with unitarity. § 1. Introduction Physical reality of particles that can travel faster than light, or tachyons as they are called nowadays, has long remained in doubt, and until very recently related problems have not attracted any serious attention of physicists. The reason for such neglect, as is well known, lies in its apparent contradiction with causality in the most naive sense of the word, that is, effect should be preceded by cause. Suppose that in a certain frame of reference there is a tachyon travelling with positive energy and forwards in time. When observed from another frame of reference, it looks as if the particle were travelling with negative energy and backwards in time, so that cause appears to be preceded by effect. In their recent paper, Bilaniuk, Deshpande and Sudarshan 1) have suggested, however, a theoretical possibility of removing the above contradiction by introducing the so-called reinterpretation principle. According to this principle, a tachyon travelling with negative energy and backwards in time is interpreted as the one travelling with positive energy and forwards in time, causality being thereby recovered .*) On the other hand, a number of authors have investigated the problem of tachyons from the viewpoint of quantum field theory. Tanaka 2) was the first to attempt such an approach, and was followed recently by Feinberg, 3) Arons and Sudarshan, 4) Dhar and Sudarshan 5) and others. The works of these authors are *) The principle is ambiguous as to the interpretation of tachyons with exactly zero energy. Since such states correspond to a domain of vanishing measure in the continuum of possible states, we expect that they do not essentially contribute to physical quantities (as far as wave packets are concerned).