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arXiv · 1904.08600

Phase ambiguity of the measure for continuum Majorana fermions

Maarten Golterman·Yigal Shamir
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Abstract

Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative lattice definition, allowing us to discuss the relation between the phase of the lattice pfaffian and the effective $θ$ angle of the theory. We also resolve an apparent paradox regarding the induced $θ$ angle when a theory of $N$ Dirac fermions in a real representation of the gauge group is re-expressed in terms of $2N$ Majorana fermions. We discuss how all this is reflected in chiral perturbation theory.

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BibTeXRIS

Maarten Golterman, Yigal Shamir. 2019-05-23. Phase ambiguity of the measure for continuum Majorana fermions. https://doi.org/10.1103/physrevd.100.034507

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