Quantum axiomatics: survey and proposal of a general realistic and operational approach

Stanley Gudder

Santiago Esteban Perez Bergliaffa, H. Vucetich, Gustavo Esteban Romero

B. Serifo Balde

Motivated by Hilbert's sixth problem on axiomatization of physics, the author is proposing a rather provocative abstract axiomatic framework called S - formalization, where S is an arbitrary physical system .The proposal is an attempt to provide a general axiomatic framework , from which mathematical frameworks of new physical theories can be formulated on firm axiomatic basis and the mathematical frameworks of subjects such as standard (nonrelativistic) quantum mechanics are naturally derived as special cases of this general axiomatic framework. Introduction

Diederik Aerts

Yu.M. Lomsadze, Sh.Yu. Lomsadze

Gabriel D. Puccini, H. Vucetich

A realistic physical axiomatic formulation of the relativistic quantum theory of fields is presented. Based on the action principle of Schwinger, the approach is developed in an aaabstract ( it does not depend on any particular representation of field operators) and covariant way for fields satisfying global gauge invariance. The field equations and the explicit expressions for the generators are deduced without using the "correspondence principle". Unlike other proofs, crossing symmetry arises in an independent way of the causality requirement. By contrast to the mathematical systems of axioms, particular emphasis on the problem of attaching a physical meaning to the formalism is handled. Arguments for a realistic interpretation in terms of "quantum fields" are advanced. Our realistic view is illustrated by regarding quantum fields as "real things" with a number of properties (e.g., interaction, symmetry properties, etc.). As a result of this conception, the fundamental variables in terms of which our axiomatics is constructed are field operators, not particles states. The advantages of our axiomatic approach are finally discussed.