Berry curvature and 4-dimensional monopole in relativistic chiral kinetic equation

Abstract: We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a 4-dimensional Euclidean Berry monopole which gives axial anomaly. By integrating out the zero-th component of the 4-momentum p, we reproduce the previous 3-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields ($F\tilde{F} \sim E.B$). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.

Berry Curvature and 4-Dimensional Monopole in Relativistic Chiral Kinetic Equation

The paper "Berry curvature and 4-dimensional monopole in relativistic chiral kinetic equation" by Chen, Pu, Wang, and Wang explores the theoretical derivation of a relativistic chiral kinetic equation with manifest Lorentz covariance. This is accomplished through an analysis utilizing Wigner functions for spin-1/2 massless fermions in a constant electromagnetic field. The approach uniquely integrates vorticity terms and establishes a relation to a 4-dimensional Euclidean Berry monopole that contributes to the axial anomaly.

Key Contributions and Findings

• Derivation Methodology: The authors adopt a novel methodology of deriving the chiral kinetic equation from Wigner functions, offering a semi-classical description of quantum transport phenomena. This perspective reveals an intrinsic link between the Berry phase and gauge invariant Wigner functions.
• Vorticity and Berry Monopole Incorporation: The kinetic equation derived incorporates features of Berry curvature akin to a magnetic field and introduces a 4-dimensional Euclidean monopole. The inclusion of vorticity terms distinguishes this approach from previous non-covariant methodologies and captures additional physical effects.
• Anomalous Conservation Laws: The paper addresses phase space continuity equations with an anomalous source term connected to electric and magnetic fields, speculating the role of the 4-dimensional monopole in Euclidean momentum space regarding interpretations of the chiral anomaly.

Theoretical and Practical Implications

• Chiral Anomaly and Berry Phase: The study provides a unified interpretation of the chiral anomaly, Berry curvature, and monopole in relativistic systems, emphasizing its significance in developing quantum transport theories and understanding gauge symmetries in particle physics.
• Quantum Transport and Astrophysical Phenomena: Implications extend to quantum field theory and hydrodynamics, enhancing models that describe phenomena like the chiral magnetic effect and its role in astrophysical contexts, including neutron star dynamics and cosmic evolution.

Speculation on Future Developments

This work lays foundational groundwork for exploring quantum chromodynamics (QCD) in extreme conditions and other relativistic fermionic systems. Potential future developments could involve computational simulations to validate theoretical predictions, exploration of analogous phenomena in condensed matter physics, and experimental endeavors in high-energy physics to observe these theoretical constructs.

Conclusion

The paper presents a comprehensive framework for understanding Berry curvature and monopoles in relativistic chiral kinetic systems, contributing significantly to the field of quantum transport and theoretical particle physics. By establishing a covariant method and addressing anomalous properties, the study enriches the discourse on chiral phenomena and their broader implications across various domains of physics research.