The Logic behind Feynman's Paths

TL;DR

This paper reformulates quantum theory by replacing classical notions of causality with a logic based on symmetries and randomness, leading to Feynman paths and new calculational rules.

Contribution

It introduces a new logical framework for quantum histories derived from symmetry principles, replacing classical trajectories with probabilistic event histories.

Findings

Derives Feynman rules from a symmetry-based logic

Connects quantum histories to Schwinger trace formula

Replaces classical causality with a symmetry-driven probabilistic approach

Abstract

The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective representations of sym- metries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random an discontinuous events. So the theory is reduced to determin- ing the probability distribution for such histories according with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.