Field theories without fundamental gauge symmetries

Abstract

By using the lack of dependence of the form of the kinetic energy for a nonrelativistic free particle as an example, it is argued that a physical law with a less extended range of application (non-relativistic energy momentum relation) often follows from a more extended one (in this case the relativistic relation) without too much dependence on the details of the latter. We extend the lesson from such examples to the ideal of random dynamics: no fundamental laws are needed to be known. Almost any random fundamental model will give the correct main features for the range of physical conditions accessible to us today (energies less than 1000 GeV) even if it is wrong in detail. This suggests the programme of attempting to ‘derive’ the various symmetries and other features of physics known today from random models at least without the feature to be derived. As an example, D. Forster, M. Ninomiya and myself ‘ derive ’ gauge invariance in this way (Forster et al ., Phys. Lett . B 94, 135 (1980)), and show that it has at least a nonzero probability for being effectively a symmetry. In fact we show that a certain nongauge-symmetric lattice model has zero mass photons for a whole range of its parameters, so that it is not necessary to fine tune it to get massless photons. It comes about by means of a formal gauge symmetry achieved by introducing a superfluous number of field variables. The achievements in our programme of random dynamics up till now are briefly reviewed. In particular, Lorentz invariance may be understood as a low energy phenomenon (S. Chadha, M. Ninomiya and myself). An analogy between the development of physics as one goes to lower and lower energies and that of living species through the history of the Earth is put forward.