Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum kinetic theory for spin-1/2 fermions in Wigner function formalism
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which satisfy 32 coupled equations. For massless fermions, the number of independent equations can be significantly reduced due to the decoupling of left-handed and right-handed particles. It can be proved that out of many components of Wigner functions and their coupled equations, only one kinetic equation for the distribution function is independent. This is called the disentanglement theorem for Wigner functions of chiral fermions. For massive fermions, it turns out that one particle distribution function and three spin distribution functions are independent and satisfy four kinetic equations. Various chiral and spin effects such as chiral magnetic and votical effects, the chiral seperation effect, spin polarization effects can be consistently described in the formalism.
rate research
Read More
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 to 4 independent transport equations. We solve 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.
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The Wigner function and its kinetic equations are expanded in terms of the generators of Clifford algebra and a complicated system of partial differential equations is obtained. We prove that some component equations are automattically satisfied if the rest ones are fulfilled. In this thesis two methods are proposed for calculating the Wigner function, which are proved to be equivalent. The Wigner function is analytically calculated following the standard second-quantization procedure in the following cases: free fermions with or without spin imbalance, in constant magnetic field, in constant electric field, and in constant parallel electromagnetic field. Strong-field effects, such as the Landau levels and Schwinger pair-production are reproduced using the Wigner function approach. For an arbitrary space-time dependent field configuration, a semi-classical expansion with respect to the reduced Plancks constant $hbar$ is performed. We derive general expressions for the Wigner function components at linear order in $hbar$, in which order the spin corrections start playing a role. A generalized Bargmann-Michel-Telegdi (BMT) equation and a generalized Boltzmann equation are obtained for the undetermined polarization density and net fermion number density, which can be used to construct spin-hydrodynamics in the future. We also make a comparison between analytical results and the ones from semi-classical expansion, which shows coincidence for weak electromagnetic fields and small spin imbalance.
We find that the recently developed kinetic theories with spin for massive and massless fermions are smoothly connected. By introducing a reference-frame vector, we decompose the dipole-moment tensor into electric and magnetic dipole moments. We show that the axial-vector component of the Wigner function contains a contribution from the transverse magnetic dipole moment which accounts for the transverse spin degree of freedom (DOF) and vanishes smoothly in the massless limit. As a result, the kinetic equations, describing four DOF for massive fermions, becomes smoothly the chiral kinetic equations describing two DOF in the massless limit. We also confirm the small-mass behavior of the Wigner function by explicit calculation using a Gaussian wave packet.
Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.
We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
