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FUNCTIONAL INTEGRAL REPRESENTATIONS AND GOLDEN–THOMPSON INEQUALITIES IN BOSON–FERMION SYSTEMS
| Title: | FUNCTIONAL INTEGRAL REPRESENTATIONS AND GOLDEN–THOMPSON INEQUALITIES IN BOSON–FERMION SYSTEMS |
| Authors: | ARAI, ASAO Browse this author →KAKEN DB |
| Keywords: | boson–fermion system | | conditional oscillator measure | | Dirac operator | | functional integral | | Golden–Thompson inequality | | ground state energy | | supersymmetric quantum mechanics |
| Issue Date: | 19-Sep-2013 |
| Publisher: | World Scientific Publishing |
| Journal Title: | Reviews in Mathematical Physics |
| Volume: | 25 |
| Issue: | 08 |
| Start Page: | 1350015 |
| Publisher DOI: | 10.1142/S0129055X13500153 |
| Abstract: | For a general class of boson–fermion Hamiltonians H acting in the tensor product Hilbert space L2(Rn) ^(Cr) of L2(Rn) and the fermion Fock space ^(Cr) over Cr (n, r 2 N), we establish, in terms of an n-dimensional conditional oscillator measure, a functional integral representation for the trace Tr (F zNf e¡tH) (F 2 L1(Rn), z 2 Cnf0g, t > 0), where Nf is the fermion number operator on ^(Cr). We prove a Golden–Thompson type inequality for jTr (F zNf e¡tH)j. Also we discuss applications to a model in supersymmetric quantum mechanics and present an improved version of the Golden–Thompson inequality in supersymmetric quantum mechanics given by Klimek and Lesniewski (Lett. Math. Phys. 21 (1991), 237–244). An upper bound for the number of the supersymmetric states is given as well as a sufficient condition for the spontaneous supersymmetry breaking. Moreover, we derive a functional integral representation for the analytical index of a Dirac type operator on Rn (Witten index) associated with the supersymmetric quantum mechanical model. |
| Rights: | Electronic version of an article published as Rev. Math. Phys., 25, 1350015 (2013) [43 pages] [DOI: 10.1142/S0129055X13500153] [Copyright© 2013 World Scientific Publishing Co.] [http://www.worldscientific.com/worldscinet/rmp] |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/53384 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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