Thermodynamics of Bosonic Higher Spin Fields

TL;DR

This work analyzes the thermodynamics of free massless bosonic higher-spin fields in $d \ge 4$ Minkowski spacetime using a Feynman path-integral approach. By formulating the Fronsdal-based HS fields with gauge constraints and performing Gaussian integration, it derives the partition function $Z=(\det \beta s\Box)^{-1/2}$ and computes the associated thermodynamic quantities $F$, $E$, and $S$ under dimensional regularization. The results show a spin-independent average energy that mirrors the blackbody spectrum and can be related to the cosmic microwave background at $T=2.7\,$K, while the entropy demonstrates a self-duality with the Klein-Gordon scalar theory in $d=4$. UV divergences are removed by the regularization procedure, whereas IR divergences scale with volume. Overall, the paper highlights a thermodynamic duality between higher-spin and scalar fields and links HS thermodynamics to familiar thermal spectra and holographic-like dualities, with implications for holographic ideas and finite-temperature field theory.

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.