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
-
81Q60 Supersymmetric quantum mechanics
- Subjects
- Dates
-
Issue 21 (30 May 2008)
Received 5 February 2008, in final form 13 April 2008
Published 6 May 2008
-
Dyson–Maleev representation of nonlinear sigma models
D A Ivanov and M A Skvortsov 2008 J. Phys. A: Math. Theor. 41 215003
-
Ward identity and electrical conductivity in hot QED
Gert Aarts and Jose M. Martínez Resco JHEP11(2002)022
-
Transport coefficients in large Nf gauge theories with massive fermions
Gert Aarts and Jose M. Martínez Resco JHEP03(2005)074
-
Meson spectral functions with chirally symmetric lattice fermions
UKQCD Collaboration et al JHEP02(2007)062
-
Shear viscosity in the O(N) model
Gert Aarts and Jose M. Martínez Resco JHEP02(2004)061
-
Transport coefficients, spectral functions and the lattice
Gert Aarts and Jose María Martínez Resco JHEP04(2002)053
-
Stochastic quantization at finite chemical potential
Gert Aarts and Ion-Olimpiu Stamatescu JHEP09(2008)018
-
Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
Gert Aarts JHEP05(2009)052
-
Influence of composition and well-width fluctuations on optical gain in (In, Ga)N multiple quantum wells
M Vehse et al 2001 Semicond. Sci. Technol. 16 406
-
Collective decoherence of cold atoms coupled to a Bose–Einstein condensate
M A Cirone et al 2009 New J. Phys. 11 103055
Users also read
What's this?- One-dimensional anyons with competing δ-function and derivative δ-function potentials
- Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies
-
Discrete
-symmetric models of scattering
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
- Exact superconformal and Yangian symmetry of scattering amplitudes