Grassmann matrix quantum mechanics
Abstract
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
 Authors:

 Institute for Advanced Study, Princeton, NJ (United States)
 Columbia Univ., New York, NY (United States); Instituut voor Theoretische Fysica, Leuven (Belgium)
 Publication Date:
 Research Org.:
 Columbia Univ., New York, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1326967
 Grant/Contract Number:
 SC0011941
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 1/N expansion; Matrix Models; Gaugegravity correspondence
Citation Formats
Anninos, Dionysios, Denef, Frederik, and Monten, Ruben. Grassmann matrix quantum mechanics. United States: N. p., 2016.
Web. doi:10.1007/JHEP04(2016)138.
Anninos, Dionysios, Denef, Frederik, & Monten, Ruben. Grassmann matrix quantum mechanics. United States. doi:10.1007/JHEP04(2016)138.
Anninos, Dionysios, Denef, Frederik, and Monten, Ruben. Thu .
"Grassmann matrix quantum mechanics". United States. doi:10.1007/JHEP04(2016)138. https://www.osti.gov/servlets/purl/1326967.
@article{osti_1326967,
title = {Grassmann matrix quantum mechanics},
author = {Anninos, Dionysios and Denef, Frederik and Monten, Ruben},
abstractNote = {We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.},
doi = {10.1007/JHEP04(2016)138},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2016,
place = {United States},
year = {2016},
month = {4}
}
Web of Science