Quantization of fluctuations in DSR: the two-point function and beyond

TL;DR

This paper demonstrates that in de Sitter momentum space, the two-point function can be factorized into a delta function and an energy-dependent term, revealing scale-invariance of vacuum fluctuations at high energies and uncovering unique structures in higher-order correlators.

Contribution

It provides a novel expression for the two-point function in DSR and analyzes the structure of the three-point function, advancing understanding of quantum fluctuations in deformed spacetime models.

Findings

Two-point function factorizes into delta and energy-dependent parts

Vacuum fluctuations are scale-invariant at high energies with dimensionality running

Three-point function exhibits 'open triangle' structure

Abstract

We show that the two-point function of a quantum field theory with de Sitter momentum space (herein called DSR) can be expressed as the product of a standard delta function and an energy-dependent factor. This is a highly non-trivial technical result in any theory without a preferred frame. Applied to models exhibiting running of the dimensionality of space, this result is essential in proving that vacuum fluctuations are generally scale-invariant at high energies whenever there is running to two dimensions. This is equally true for theories with and without a preferred frame, with differences arising only as we consider higher order correlators. Specifically, the three-point function of DSR has a unique structure of "open triangles", as shown here.