Sergey M Sergeev 2009 J. Phys. A: Math. Theor. 42 295206 doi:10.1088/1751-8113/42/29/295206
Classical integrable field theories in discrete (2 + 1)-dimensional spacetime
Sergey M Sergeev
Show affiliationsWe study the 'circular net' (discrete orthogonal net) equations for the angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of the Lagrangian density. There are four distinct regimes for fields and spectral parameters classified by four types of spherical or hyperbolic triangles. Nonzero external spectral parameters provide the existence of field-theoretical ground states and soliton excitations. Spectral parameters of a spherical triangle correspond to a statistical mechanics; spectral parameters of hyperbolic triangles correspond to three different field theories with massless anisotropic dispersion relations.
- PACS
-
11.10.Ef Lagrangian and Hamiltonian approach
11.10.Jj Asymptotic problems and properties
11.10.Kk Field theories in dimensions other than four
05.30.Fk Fermion systems and electron gas
- MSC
-
81U30 Dispersion theory, dispersion relations
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
- Subjects
-
Quantum gases, liquids and solids
- Dates
-
Issue 29 (24 July 2009)
Received 23 April 2009
Published 3 July 2009
-
Classical integrable field theories in discrete (2 + 1)-dimensional spacetime
Sergey M Sergeev 2009 J. Phys. A: Math. Theor. 42 295206
-
Quantum frustration of dissipation by a spin bath
D D Bhaktavatsala Rao et al 2008 New J. Phys. 10 115017
-
In search of fundamental discreteness in (2 + 1)-dimensional quantum gravity
T G Budd and R Loll 2009 Class. Quantum Grav. 26 185011
-
Peer review statement
2008 J. Phys.: Conf. Ser. 189 011002
-
2p x-ray absorption of iron-phthalocyanine
Piter S Miedema et al 2009 J. Phys.: Conf. Ser. 190 012143
-
An(1) affine Toda field theories with integrable boundary conditions revisited
Anastasia Doikou JHEP05(2008)091
-
Thermodynamic properties of Holstein polarons and the effects of disorder
A N Das and S Sil 2008 J. Phys.: Condens. Matter 20 345222
-
Novel nanostructure and magnetic properties of Co–Fe–Hf–O films
Nguyen Duy Ha et al 2007 Nanotechnology 18 155705
-
An anisotropic phase-field crystal model for heterogeneous nucleation of ellipsoidal colloids
R Prieler et al 2009 J. Phys.: Condens. Matter 21 464110
-
LISA parameter estimation of supermassive black holes
Miquel Trias and Alicia M Sintes 2008 Class. Quantum Grav. 25 184032
Users also read
What's this?- The large-N limit of PT-symmetric O(N) models
- Continuum states in generalized Swanson models
- Clifford groups of quantum gates, BN-pairs and smooth cubic surfaces
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
- Scattering amplitudes and Wilson loops in twistor space
super-Yang–Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops