Conservation laws for linear equations on quantum Minkowski spaces
نویسنده
چکیده
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for ∗-invariant equations. The derived method is then applied to Klein-Gordon, Dirac and wave equations on different classes of Minkowski spaces. In the examples also symmetry operators for these equations are obtained. They include quantum deformations of classical symmetry operators as well as an additional operator connected with deformation of the Leibnitz rule in non-commutative differential calculus.
منابع مشابه
Classification of local conservation laws of Maxwell’s equations
A complete and explicit classification of all independent local conservation laws of Maxwell’s equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic conservation laws associated to the conserved stress-energy and zilch tensors, there are also chiral quadratic conservation laws which are associated to a new conserved...
متن کاملSymmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation
In this paper Lie point symmetries, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation are investigated. First of all Lie symmetries are obtained by using the general method based on invariance condition of a system of differential equations under a prolonged vector field. Then the structure of symmetry ...
متن کاملConservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general method include equations on quantum plane, supersymmetric equations for chiral and antichiral supermultiplets as well as auxiliary equations of integrable model...
متن کاملNoether Currents for Bosonic Branes
We consider a relativistic brane propagating in Minkowski spacetime described by any action which is local in its worldvolume geometry. We examine the conservation laws associated with the Poincaré symmetry of the background from a worldvolume geometrical point of the view. These laws are exploited to explore the structure of the equations of motion. General expressions are provided for both th...
متن کاملRegularity through Approximation for Scalar Conservation Laws∗
In this paper it is shown that recent approximation results for scalar conservation laws in one space dimension imply that solutions of these equations with smooth, convex fluxes have more regularity than previously believed. Regularity is measured in spaces determined by quasinorms related to the solution’s approximation properties in L1(R) by discontinuous, piecewise linear functions. Using a...
متن کامل