Formulation of Relativistic Dissipative Spin Hydrodynamics

Abstract

The primary objective of this thesis is to develop a consistent theoretical framework of dissipative hydrodynamics for a relativistic fluid with spin - hereafter referred to as relativistic dissipative spin hydrodynamics. In this framework, the dynamical description of a relativistic fluid requires a new macroscopic variable, the spin density, which is associated with a spin tensor. This tensor, defined as the expectation value of a rank-3 tensor operator in quantum field theory, contributes to the system's total angular momentum. The need for such a theory is motivated by recent measurements of spin polarization of hadrons produced in non-central relativistic heavy-ion collisions. Two distinct formulation methods are employed. The first is grounded in covariant thermodynamics and extends the conventional Navier-Stokes and M\"uller-Israel-Stewart theories of relativistic hydrodynamics by incorporating a spin tensor. The second is based on principles of relativistic quantum statistical mechanics, building upon and generalizing the foundational Zubarev approach. Both formulations aim to construct a closed system of evolution equations for the macroscopic variables and, via an entropy-current analysis, to identify the dissipative currents and their associated transport coefficients. These two approaches provide different perspectives for future applications focused on spin polarization measurements. Beyond its phenomenological relevance, the theory also opens several avenues for further theoretical developments. These include the verification of the thermodynamic relations employed in the first formulation method using microscopic frameworks, as well as a deeper understanding of the emerging transport coefficients - particularly those associated with the spin tensor - through microscopic modeling or data-driven parameter extraction.