The foundations of quantum theory and its possible generalizations

TL;DR

This paper explores potential generalizations of quantum theory, focusing on Lorentz invariance and divergence issues, by reviewing Lindblad's equation, introducing a Tomonaga-Schwinger-like equation, and considering tachyonic fields.

Contribution

It presents a novel approach to generalizing quantum theory using a Tomonaga-Schwinger-like equation and tachyonic fields to address divergences and ensure Lorentz invariance.

Findings

Introduced a Tomonaga-Schwinger-like equation for quantum systems

Analyzed the use of tachyonic fields to resolve divergences

Reviewed Lindblad's equation in the context of quantum generalizations

Abstract

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the statistical operator is reviewed. The Tomonaga-Schwinger like equation of this type is introduced to establish Lorentz invariance. The application of tachyonic field to overcome divergences arising in this equation is analyzed. Other approaches to the problem are shortly discussed.