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Title: Phase ambiguity of the measure for continuum Majorana fermions

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.

Authors:
;
Publication Date:
Research Org.:
San Francisco State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Israel Science Foundation (ISF)
OSTI Identifier:
1550589
Alternate Identifier(s):
OSTI ID: 1594606
Report Number(s):
arXiv:1904.08600v3
Journal ID: ISSN 2470-0010; PRVDAQ; 034507
Grant/Contract Number:  
FG03-92ER40711; SC0013682; 491/17
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective field theory; Lattice field theory; Path integrals

Citation Formats

Golterman, Maarten, and Shamir, Yigal. Phase ambiguity of the measure for continuum Majorana fermions. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.034507.
Golterman, Maarten, & Shamir, Yigal. Phase ambiguity of the measure for continuum Majorana fermions. United States. doi:10.1103/PhysRevD.100.034507.
Golterman, Maarten, and Shamir, Yigal. Fri . "Phase ambiguity of the measure for continuum Majorana fermions". United States. doi:10.1103/PhysRevD.100.034507.
@article{osti_1550589,
title = {Phase ambiguity of the measure for continuum Majorana fermions},
author = {Golterman, Maarten and Shamir, Yigal},
abstractNote = {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.},
doi = {10.1103/PhysRevD.100.034507},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.034507

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Works referenced in this record:

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