ESTENSIONE DELLA TEORIA QUANTISTICA DI CAMPO A TEORIA DI AUTOMA CELLULARE QUANTISTICO

Abstract

In the present note I will briefly report recent results on the novel field theory based on the information-theoretical paradigm. This program continues the previous one on the axiomatic derivation of quantum theory from information-theoretical principles, of which I presented a note on January 31st 2008. The passage from the quantum theory of abstract systems to the theory of fields is achieved by adding to the axioms of quantum theory new general principles for the network of interation among a denumerable set of quantum systems. Such principles can be synthesized with the requirement of minimal complexity of the quantum algorithm describing the physical law. From general principles such as homogeneity, isotropy, locality, linearity, and unitarity of the interaction network, along with minimal dimension of the field vector, one derives the free quantum field theory, namely Weyl, Dirac, and Maxwell fields. The principles lead to a description in terms of a quantum cellular automaton on the Cayley graph of a group. The advantages of the new theory are numerous. For example the theory tautologically solves all the problems originating from the continuum, such as the ultraviolet divergencies, the localization problem, and causality violations. The mechanics itself is not assumed, but it is a consequence of the principles, and the theory is quantum ab initio, namely it does not need quantization of a classical field theory. Lorentz covariance is not assumed, but follows itself from the principles, in the relativistic limit of small wavevectors. The notion of reference system is restated in terms of irreducible representation of the quantum automaton. Finally, the new theory, derived from purely mathematical principles–whence with adimensional variables–contains itself the units of measure for distance, time, and mass, which are given in terms of extremal values of the variables, which are in principle experimentally detectable. Also effects with GR flavor emerge from the automaton theory, such as an upper bound for the Dirac particle rest-mass (from the unitariety condition), where the dispersion relation becomes completely flat, in strict analogy with the notion of mini black hole.