Solutions of q-deformed equations with quantum conformal symmetry
We consider the construction of explicit solutions of a hierarchy of q-deformed equations which are (conditionally) quantum conformal invariant. We give two types of solutions--polynomial solutions and solutions in terms of q-deformation of the plane wave. We give a q-deformation of the plane wave a...
Saved in:
Published in | AIP conference proceedings Vol. 453; no. 1 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
United States
15.12.1998
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We consider the construction of explicit solutions of a hierarchy of q-deformed equations which are (conditionally) quantum conformal invariant. We give two types of solutions--polynomial solutions and solutions in terms of q-deformation of the plane wave. We give a q-deformation of the plane wave as a formal power series in the noncommutative coordinates of q-Minkowski space-time and four-momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d'Alembert equation on the q-Lorentz covariant momentum cone. On the other hand, this q-plane wave is not an exponent or q-exponent. Thus, it differs conceptually from the classical plane wave and may serve as a its regularization. Using this we give also solutions of the massless Dirac equation involving two conjugated q-plane waves--one for the neutrino, the other for the antineutrino. It is also interesting that the neutrino solutions are deformed only through the q-pane wave, while the prefactor is classical. Thus, we can speak of a definite left-right asymmetry of the quantum conformal deformation of the neutrino-antineutrino system. |
---|---|
ISSN: | 0094-243X 1551-7616 |
DOI: | 10.1063/1.57120 |