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We discuss parity violating effects in relativistic quantum theory and theiranalogues in effective field theory of superfluid 3He-A. A mixedaxial-gravitational Chern-Simons term in the relativistic effective action andits condensed matter analog are responsible for the chiral fermion flux alongthe rotation axis of the heat bath in relativistic system and for the unusualOmega-odd dependence of the zero-temperature density of the normal component onthe rotation velocity in 3He-A.Comment: 6 pages, RevTex file, no figures, modified after referee repor

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Macroscopic parity violating effects and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">He</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">A</mml:mi></mml:math>

Macroscopic parity violating effects and3He−A