# From path integrals to dynamical algebras: a macroscopic view of quantum physics

## TL;DR

This paper presents a novel approach linking path integrals to dynamical algebras, providing a new foundational perspective on quantum physics and its emergence from algebraic relations, applicable to particles and field theories.

## Contribution

It introduces a new algebraic framework derived from path integral relations, offering insights into quantum foundations and extending to quantum field theories.

## Key findings

- Derives a dynamical algebra from path integral relations
- Shows quantum mechanics emerges from this algebraic structure
- Applicable to both non-relativistic particles and quantum field theories

## Abstract

The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its invariance properties under variations of the action. These relations determine a dynamical algebra of bounded operators which encodes all properties of the corresponding quantum theory. This novel approach is applied to non-relativistic particles, where quantum mechanics emerges from it. The method works also in interacting quantum field theories and sheds new light on the foundations of quantum physics.