Macroscopic Parity-Violating Effects
The chiral anomaly phenomenon in relativistic quantum field theory can also be mapped to the angular momentum paradox in 3He-A, which has possibly a common origin with the anomaly in the spin structure of hadrons. To relate the chiral anomaly and angular momentum paradox in 3He-A, it is necessary to consider the parity effects which occur for the system of chiral fermions under rotation. This chapter discusses macroscopic parity violation, mixed axial gravitational Chern–Simons term, parity-violating current, parity-violating action in terms of gravimagnetic field, orbital angular momentum in 3He-A, and the odd current in 3He-A — sensitivity of the normal component density to the direction of rotation, which is the counterpart of the parity-violating effects in relativistic theories with chiral fermions. There is no real parity violation in 3He-A. However, a non-zero expectation value of the axial vector of the orbital angular momentum indicates a spontaneously broken reflectional symmetry, and an inner observer living in 3He-A would consider this effect as true parity violating.
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