Discrete dynamical equations in minkowski space

Wave equations on q-Minkowski space

We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-LaplaceBeltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d’Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solut...

Difference Equations as Discrete Dynamical Systems

Lia Vas Discrete Dynamical Systems . Difference Equations

If values that we monitor changes during discrete periods (for example, in discrete time intervals), the formula above leads to a difference equation or a dynamical system. In this case, we are dealing with a function that depends on discrete integer values – a sequence. Recall that a sequence of real numbers (indexed by nonnegative integers) can be given by listing its terms (for example, 1, 1...

Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations

By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the lattice; (b) the emergence of the time direction on the basis of the encoding of probabilities in the lattice structure; (c) the general prescription for th...

m-Projections involving Minkowski inverse and range symmetric property in Minkowski space

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...