Symmetry preserving discretization of SL(2,R) invariant equations
نویسندگان
چکیده
Symmetry preserving discretization of SL(2,R) invariant equations Anne Bourlioux a, Raphaël Rebelo b,c and Pavel Winternitz a,b a Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec H3C 3J7, Canada. E-mail: [email protected] b Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec H3C 3J7, Canada. E-mail: [email protected] c Département de Physique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec H3C 3J7, Canada. E-mail: [email protected]
منابع مشابه
Duality symmetry in four dimensional string actions
We reduce the dual version of D = 10, N = 1 supergravity coupled to n vector fields to four dimensions, and derive the SL(2, R) × O(6, 6 + n) transformations which leave the equations of motion invariant. For n = 0 SL(2, R) is also a symmetry of the action, but for n > 0 only those SL(2, R) transformations which act linearly on all fields leave the action invariant. The resulting four-dimension...
متن کاملStructure Preserving Discretizations of the Liouville Equation and their Numerical Tests
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same bound...
متن کاملAlgebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations
The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H and Ḣ right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume el...
متن کاملTwist maps for non-standard quantum algebras and discrete Schrödinger symmetries
The minimal twist map introduced by Abdesselam et al [1] for the nonstandard (Jordanian) quantum sl(2,R) algebra is used to construct the twist maps for two different non-standard quantum deformations of the (1+1) Schrödinger algebra. Such deformations are, respectively, the symmetry algebras of a space and a time uniform lattice discretization of the (1 + 1) free Schrödinger equation. It is sh...
متن کاملArea-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2, R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and ...
متن کامل