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Abstract
We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce in practice to 4 independent transport equations. We solve the modified on-shell conditions to obtain the general solution and present the corresponding transport equations in three different forms that are suitable for different purposes. We demonstrate how different spin effects arise from the kinetic theory by calculating the chiral separation effect with mass correction, the chiral anomaly from the axial current and the quantum magnetic moment density induced by vorticity and magnetic field. We also show how to generate the global polarization effect due to spin vorticity coupling. The formalism presented may serve as a practical theoretical framework to study different spin effects in relativistic fermion systems encountered in different areas such as heavy ion, astro-particle and condensed matter physics as well.
Highlights
Spin plays an essential and fascinating role to probe the underlying structure of theories in different areas of physics
We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce in practice to 4 independent transport equations
What is quite extraordinary in heavy ion collisions is that spin can emerge as a series of macroscopic collective effects such as, besides the global polarization effect (GPE) [3,4,5,6,7] observed by STAR [1,2], the chiral magnetic effect (CME) [18,19,20], the chiral vortical effect (CVE), the chiral separation effect (CSE) [21,22,23,24,25,26] and so on
Summary
Spin plays an essential and fascinating role to probe the underlying structure of theories in different areas of physics. The existing works [39,40,41,42,43,44] on RQKT for massive fermions are restricted to leading order transport equations for SPV, which is enough to deal with the vector current or energy momentum tensor to the first order in ħ They are incapable of accounting for how the GPE can be produced from vorticity and how the chiral anomaly can arise in kinetic theory for massive fermions in a self-contained manner.
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