D A Ivanov and M A Skvortsov 2008 J. Phys. A: Math. Theor. 41 215003 doi:10.1088/1751-8113/41/21/215003
Dyson–Maleev representation of nonlinear sigma models
D A Ivanov1 and M A Skvortsov2
Show affiliationsFor nonlinear sigma models in the unitary symmetry class, the nonlinear target space can be parameterized with cubic polynomials. This choice of coordinates has been known previously as the Dyson–Maleev parameterization for spin systems, and we show that it can be applied to a wide range of sigma models. The practical use of this parameterization includes simplification of diagrammatic calculations (in perturbative methods) and of algebraic manipulations (in non-perturbative approaches). We illustrate the use and specific issues of the Dyson–Maleev parameterization with three examples: the Keldysh sigma model for time-dependent random Hamiltonians, the supersymmetric sigma model for random matrices and the supersymmetric transfer-matrix technique for quasi-one-dimensional disordered wires. We demonstrate that nonlinear sigma models of unitary-like symmetry classes C and B/D also admit the Dyson–Maleev parameterization.
- PACS
- MSC
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81Q60 Supersymmetric quantum mechanics
- Subjects
- Dates
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Issue 21 (30 May 2008)
Received 5 February 2008, in final form 13 April 2008
Published 6 May 2008
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Dyson–Maleev representation of nonlinear sigma models
D A Ivanov and M A Skvortsov 2008 J. Phys. A: Math. Theor. 41 215003
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