Thermodynamics of Bosonic Higher Spin Fields

TL;DR

This paper calculates the partition function of free massless bosonic higher spin fields in Minkowski spacetime, revealing a self-duality with scalar fields and connecting the energy spectrum to blackbody radiation and cosmic microwave background data.

Contribution

It provides a novel calculation of the partition function for higher spin fields and demonstrates their self-duality with scalar fields in Minkowski spacetime.

Findings

The energy spectrum resembles blackbody radiation at various temperatures.

The entropy of higher spin fields explains the self-duality with scalar fields.

The energy spectrum aligns with the cosmic microwave background radiation.

Abstract

In this paper, I calculated the partition function of the quantum statistical system of free massless bosonic Higher spin (HS) fields on $d$-dimensional Minkowski spacetime by using the Feynman's path integral approach, it is a nontrivial result and this explain about the self-duality between the Quantum statistical system of massless free bosonic HS fields of $s \geq 2$ over $d \geq 4$ dimensional Minkowski spacetime and the Quantum statistical system of Klein-Gordon bosonic (scalar) fields on 4-dimensional Minkowski spacetime at the thermal equilibrium. However, I have been used the dimensional regularization method to calculate the free energy of this system in this calculations the ultraviolet divergences(UV) present that could be eliminated. Nevertheless, still have infrared (IR) divergences in this theory and also I discussed about the average energy and the entropy of this system over $d \geq 4$-dimensional Minkowski spacetime. In particular,the most significant result is that the average energy spectrum of quantum statistical system of massless bosonic HS fields is similar to the blackbody radiation energy spectrum at different temperatures and also it explain the Universe cosmic microwave background(CMB)radiation spectrum (COBE data) at 2.7 kelvin temperature. However, the entropy of massless free bosonic HS fields also explain the self duality between the massless free bosonic HS fields and Klein-Gordon bosonic (scalar) fields over 4-dimensional Minkowski spacetime.