Wigner function in Liouville space: A canonical formalism

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

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Necessity of negative Wigner function for tunneling

Physical Review A ◽

10.1103/physreva.102.062210 ◽

2020 ◽

Vol 102 (6) ◽

Author(s):

Yin Long Lin ◽

Oscar C. O. Dahlsten

Keyword(s):

Wigner Function

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Zilch vortical effect for fermions

Journal of High Energy Physics ◽

10.1007/jhep05(2021)070 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Artem Alexandrov ◽

Pavel Mitkin

Keyword(s):

Kinetic Theory ◽

Spin Polarization ◽

Wigner Function ◽

Microscopic Theory ◽

Chiral Media ◽

Function Formalism ◽

Chiral Effects ◽

Definition Of ◽

Theory Framework ◽

Full Analogy

Abstract We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.

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