Classification of sign-problem-free relativistic fermions on the basis of the Majorana positivity

Hayata, Tomoya (Department of Physics, Chuo University, Tokyo 112-8551, Japan) ; Yamamoto, Arata (Department of Physics, The University of Tokyo, Tokyo 113-0031, Japan)

21 April 2017

Abstract: We classify the sign-problem-free relativistic fermion actions on the basis of the Majorana representation. In the Majorana representation, the sign-problem-free condition is given by the semi-positivity of a Pfaffian. We show that the known sign-problem-free actions of the Dirac fermions, which are usually understood from the semi-positivity of a determinant, e.g., the action of quantum chromodynamics with nonzero chiral chemical potential or nonzero isospin chemical potential, can also be understood from the semi-positivity of a Pfaffian. We also derive new classes of the sign-problem-free relativistic fermion actions with Majorana-type source terms.


Published in: PTEP 2017 (2017) 043B08
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/ptx040
arXiv: 1701.07182
License: CC-BY-3.0



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