The normal ordering formulae for powers of the boson number operator n̂ are extended to deformed bosons. It is found that for the “M-type” deformed bosons, which satisfy aa− qaa = 1, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the ca...

Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity ...

In this talk, instantons are discussed in the presence of Lorentz violation. Conventional topological arguments are applied to classify the modified solutions to the Yang-Mills equations according to the topological charge. Explicit perturbations to the instantons are calculated in detail for the case of unit topological charge.

The non-perturbation and perturbation structures of the q-deformed probability currents are studied. According to two ways of realizing the q-deformed Heisenberg algebra by the undeformed operators, the perturbation structures of two q-deformed probability currents are explored in detail. Locally the structures of two perturbation q-deformed probability currents are different, one is explicitly...

By using the theory of deformed quantum mechanics, we study the deformed light beam theoretically. The deformed beam quality factor M2 q is given explicitly under the case of deformed light in coherent state. When the deformation parameter q being a root of unity, the beam quality factor M2 q ≤ 1. PACS number(s): 42.60Jf, 42.65Jx, 03.65.-w Typeset using REVTEX ∗The project supported by the Nati...

Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schrödinger equation are analyzed. General representations of the additional momentum-dependent interaction originating from the q-deformed effects are presented in two approaches. As examples, such additional interactions relate...