2004/08/18 by P. Narayana Swamy
Physics and Astronomy · #hep-th
published as Physica A353 (2005) 119-132 · 14 pages, LateX, submitted for publication
arxiv created 2004/08/18 · arxiv updated 2009/12/01
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this formalism in terms of basic numbers familiar from the theory of quantum groups. Expressions for the Hamiltonian and momentum arising from deformed Heisenberg relations are obtained and their consequences investigated. The energy momentum properties of the vacuum state are studied. The commutation relation for the fields is shown to involve polarization sums more intricate than those encountered in standard quantum electrodynamics, thus requiring explicit representations of polarization vectors. The electric field commutation rules are investigated under simplifying assumptions of polarization states, and the commutator in the deformed theory in this case is shown to be reminiscent of the coordinate-momentum uncertainty relation in the theory of q-deformed quantum oscillators.