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...

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Bibliographic Details
Published inAIP conference proceedings Vol. 453; no. 1
Main Authors Dobrev, V. K., Kostadinov, B. S., Petrov, S. T.
Format Journal Article
LanguageEnglish
Published United States 15.12.1998
Subjects
ALGEBRA
ANTINEUTRINOS
ASYMMETRY
COMMUTATION RELATIONS
CONFORMAL INVARIANCE
DIRAC EQUATION
MATHEMATICAL SOLUTIONS
MINKOWSKI SPACE
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POLYNOMIALS
POWER SERIES
QUANTUM FIELD THEORY
SPACE-TIME
SPIN
WAVE FUNCTIONS
WAVE PROPAGATION
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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