A $(D_\tau,D_x)$-manifold with $N$-correlators of $N_t$-objects

TL;DR

This paper introduces a mathematical formalism for complex manifolds with multi-type correlators, applicable across cosmological and quantum scales, using tools from physics, topology, and statistics.

Contribution

It develops a novel formalism combining field theory, topology, and algebra to analyze multi-object correlators on manifolds across various scales.

Findings

Formalism applicable from astronomical to quantum scales.

Incorporates cross correlations and contaminants in the model.

Provides intuitive examples illustrating the formalism's applicability.

Abstract

In this paper, we describe a mathematical formalism for a $(D_\tau,D_x)$-dimensional manifold with $N$-correlators of $N_t$ types of objects, with cross correlations and contaminants. In particular, we build this formalism using simple notions of mathematical physics, field theory, topology, algebra, statistics n-correlators and Fourier transform. We discuss the applicability of this formalism in the context of cosmological scales, i.e. from astronomical scales to quantum scales, for which we give some intuitive examples.