Odd coset quantum mechanics

Evgeny Ivanov; Luca Mezincescu; Anatoly Pashnev; Paul K. Townsend

doi:10.1016/S0370-2693(03)00393-9

Odd coset quantum mechanics

Evgeny Ivanov, Luca Mezincescu, Anatoly Pashnev, Paul K. Townsend

Physics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The standard quantum states of n complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same 'free-fermion' model has a non-linearly realized SU(n|1) symmetry; it can be viewed as the mechanics of a 'particle' on the Grassmann-odd coset space SU(n|1)/U(n). We implement a quantization of this model for which the states with non-zero norm transform as a representation of SU(n|1), the representation depending on the U(1) charge of the wave-function. For n = 2 the wave-function can be interpreted as a BRST superfield.

Original language	English (US)
Pages (from-to)	175-182
Number of pages	8
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	566
Issue number	1-2
DOIs	https://doi.org/10.1016/S0370-2693(03)00393-9
State	Published - Jul 24 2003

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1016/S0370-2693(03)00393-9

Fingerprint Dive into the research topics of 'Odd coset quantum mechanics'. Together they form a unique fingerprint.

Cite this

@article{0a0ded3cf83647209a699cbb396d051a,

title = "Odd coset quantum mechanics",

abstract = "The standard quantum states of n complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same 'free-fermion' model has a non-linearly realized SU(n|1) symmetry; it can be viewed as the mechanics of a 'particle' on the Grassmann-odd coset space SU(n|1)/U(n). We implement a quantization of this model for which the states with non-zero norm transform as a representation of SU(n|1), the representation depending on the U(1) charge of the wave-function. For n = 2 the wave-function can be interpreted as a BRST superfield.",

author = "Evgeny Ivanov and Luca Mezincescu and Anatoly Pashnev and Townsend, {Paul K.}",

note = "Funding Information: We thank S. Gukov, S. Krivonos, M. Berkooz, and L. Susskind, for helpful discussions. L.M. thanks the theory group at JINR, the physics department of the Weizmann Institute, the GR group of DAMTP, and the TG of Stanford University, for hospitality and partial financial support. L.M. was supported in part by the National Science Foundation under grant PHY-9870101. E.I. and A.P. acknowledge a partial support from INTAS grant No. 00-0254. E.I. was partially supported by grants DFG No. 436 RUS 113/669, RFBR-DFG 02-02-04002 and RFBR-CNRS 01-02-22005. ",

year = "2003",

month = jul,

day = "24",

doi = "10.1016/S0370-2693(03)00393-9",

language = "English (US)",

volume = "566",

pages = "175--182",

journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",

issn = "0370-2693",

publisher = "Elsevier",

number = "1-2",

}

TY - JOUR

T1 - Odd coset quantum mechanics

AU - Ivanov, Evgeny

AU - Mezincescu, Luca

AU - Pashnev, Anatoly

AU - Townsend, Paul K.

N1 - Funding Information: We thank S. Gukov, S. Krivonos, M. Berkooz, and L. Susskind, for helpful discussions. L.M. thanks the theory group at JINR, the physics department of the Weizmann Institute, the GR group of DAMTP, and the TG of Stanford University, for hospitality and partial financial support. L.M. was supported in part by the National Science Foundation under grant PHY-9870101. E.I. and A.P. acknowledge a partial support from INTAS grant No. 00-0254. E.I. was partially supported by grants DFG No. 436 RUS 113/669, RFBR-DFG 02-02-04002 and RFBR-CNRS 01-02-22005.

PY - 2003/7/24

Y1 - 2003/7/24

N2 - The standard quantum states of n complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same 'free-fermion' model has a non-linearly realized SU(n|1) symmetry; it can be viewed as the mechanics of a 'particle' on the Grassmann-odd coset space SU(n|1)/U(n). We implement a quantization of this model for which the states with non-zero norm transform as a representation of SU(n|1), the representation depending on the U(1) charge of the wave-function. For n = 2 the wave-function can be interpreted as a BRST superfield.

AB - The standard quantum states of n complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same 'free-fermion' model has a non-linearly realized SU(n|1) symmetry; it can be viewed as the mechanics of a 'particle' on the Grassmann-odd coset space SU(n|1)/U(n). We implement a quantization of this model for which the states with non-zero norm transform as a representation of SU(n|1), the representation depending on the U(1) charge of the wave-function. For n = 2 the wave-function can be interpreted as a BRST superfield.

UR - http://www.scopus.com/inward/record.url?scp=0037481695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037481695&partnerID=8YFLogxK

U2 - 10.1016/S0370-2693(03)00393-9

DO - 10.1016/S0370-2693(03)00393-9

M3 - Article

AN - SCOPUS:0037481695

VL - 566

SP - 175

EP - 182

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -