Non-Relativistic Limit of Dirac Theory in Curved Spacetime with Implications for Spin Polarization in Heavy-Ion Collisions

In this study, we investigate the non-relativistic limit of Dirac theory in curved spacetime. Previous research has utilized curved spacetime to model the effects of temperature gradients [1] and rotation [2], such as in studies on thermoelectric effects using gravitational fields [3] and on spin-rotation interactions [4]. These approaches, however, are limited to specific metric configurations and thus lack general applicability. Our work addresses this gap by creating a generalized framework incorporating higher-order relativistic effects and accommodating time-dependent metric tensors. Specifically, we decompose the spinor field in Dirac theory into particle and antiparticle components, simplifying calculations by eliminating degrees of freedom associated with the antiparticle.

This framework has important implications for Λ particle spin polarization in relativistic heavy-ion collision experiments. It allows us to demonstrate that the chiral vortical effect (CVE) and shear-induced polarization (SIP) emerge correctly from non-relativistic Dirac theory, even when Lorentz symmetry is broken. This calculation provides a concrete application of our current formulation.

[1] J. M. Luttinger, Phys. Rev. 135, A1505 (1964). [2] F. W. Hehl et al., Phys. Rev. D 42, 2045 (1990).

[3] T. Qin et al., Phys. Rev. Lett. 107, 236601 (2011). [4] M. Matsuo et al., Phys. Rev. Lett. 106, 076601 (2011).