Phase ambiguity of the measure for continuum Majorana fermions

Golterman, Maarten; Shamir, Yigal

doi:10.1103/PhysRevD.100.034507

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:: Golterman, Maarten; Shamir, Yigal

Publication Date:: 2019-08-09

Research Org.:: San Francisco State Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); 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.

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                    Golterman, Maarten, & Shamir, Yigal. Phase ambiguity of the measure for continuum Majorana fermions.  United States.  https://doi.org/10.1103/PhysRevD.100.034507

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                    Golterman, Maarten, and Shamir, Yigal. Fri .  
"Phase ambiguity of the measure for continuum Majorana fermions".  United States.  https://doi.org/10.1103/PhysRevD.100.034507.

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@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}

}

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Works referenced in this record:

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Title: Phase ambiguity of the measure for continuum Majorana fermions

Abstract

Citation Formats

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