open access

https://hdl.handle.net/2115/53384

FUNCTIONAL INTEGRAL REPRESENTATIONS AND GOLDEN–THOMPSON INEQUALITIES IN BOSON–FERMION SYSTEMS

英語

supersymmetric quantum mechanics

2013-09-19

World Scientific Publishing

Reviews in Mathematical Physics

25(08)

1350015

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.

学術雑誌論文

Accepted Manuscript

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]

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