Pawel Maslanka

More about the q-deformed Poincaré algebra

Abstract The recently proposed deformed Poincare algebra is considered. Its structure is clarified and “unitary” representations are found. The contraction to the deformed Galilei algebra is performed. The three-dimensional counterpart is discussed.

Modified Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.

The Kappa-Weyl group and its algebra

The

kappa-deformation of Poincare superalgebra with classical Lorentz subalgebra and its graded bicrossproduct structure

\kappa -

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Poincare group and its algebra in an arbitrary basis are constructed. The

Canonical formalism and quantization of the perturbative sector of higher-derivative theories

\kappa -

Representations of generalized oscillator algebra

de\-formation of the Weyl group and its algebra in any dimensions and in the reference frame in which

A note on non-integrable phases and coherent states

g_{00}=0

Projective representations of k-Galilei group

are discussed.

Heisenberg algebra for the restricted Landau problem

The kappa-deformed D=4 Poincare superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the kappa-deformed D=4 Poincare superalgebra can be written as a graded bicrossproduct. We show that the kappa-deformed D=4 superalgebra acts covariantly on a kappa-deformed chiral superspace.