Non-relativistic transport from frame-indifferent kinetic theory

Kinetic theory provides the microscopic foundation for fluid 
dynamics and transport phenomena. While its relativistic formulation is 
well established, a fully covariant description of non-relativistic 
systems remains largely unexplored. In this talk, I will present a 
covariant formulation of kinetic theory based on Newton-Cartan 
geometry—the natural geometric framework for non-relativistic gravity. 
After a brief introduction to the essential elements of Newton-Cartan 
geometry, I will discuss the dynamics of point particles and derive the 
corresponding Boltzmann equation in a manifestly covariant form. I will 
then demonstrate how exact conservation laws and the equilibrium 
distribution function naturally emerge within this framework. Finally, I 
will outline the derivation of covariant hydrodynamic equations and 
first-order constitutive relations. To conclude, I will show how this 
geometric approach uses modern symmetry principles to resolve the 
longstanding frame-dependence paradox in kinetic theory.