Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-05-18
Physics
High Energy Physics
High Energy Physics - Theory
17 pages,v3. Additional explanations and new references added, improper notation and two formulae corrected
Scientific paper
We introduce the free quantum noncommutative fields as described by braided tensor product. The multiplication of such fields is decomposed into three operations, describing the multiplication in the algebra M of functions on noncommutative space-time, the product in the algebra H of deformed field oscillators, and the braiding by factor Psi_{M,H} between algebras M and H. For noncommutativity generated by the twist factor we shall employ the star-product realizations of the algebra M in terms of functions on standard Minkowski space. The covariance of the noncommutative quantum fields under deformed Poincare symmetries is described by the algebraic covariance conditions which are equivalent to the deformation of generalized Heisenberg equations on Poincare group manifold. We shall calculate the covariant braided field commutator, which for free quantum noncommutative fields provides the field quantization condition and is given by standard Pauli-Jordan function. For ilustration of our new scheme we present explicit calculations for the well-known case in the literature of canonically deformed free quantum fields.
Lukierski Jerzy
Woronowicz Mariusz
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