[time 517] Non-commutative infinities

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 5 Aug 1999 09:55:17 +0300 (EET DST)

Dear Stephen and all,

I promised the abstract about the paper relating to the infinities
of the QFT in noncommutative geometry. Here it finally is.

High Energy Physics - Theory, abstract


Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry

Authors: M. Chaichian, A. Demichev, P. Presnajder
Comments: LaTeX, 26 pages
Report-no: HIP-1999-19/TH

     We study properties of a scalar quantum field theory on the
two-dimensional noncommutative plane with $E_q(2)$ quantum
     symmetry. We start from the consideration of a firstly quantized
quantum particle on the noncommutative plane. Then we define
     quantum fields depending on noncommutative coordinates and construct
a field theoretical action using the $E_q(2)$-invariant
     measure on the noncommutative plane. With the help of the partial
wave decomposition we show that this quantum field theory
     can be considered as a second quantization of the particle theory on
the noncommutative plane and that this field theory has
     (contrary to the common belief) even more severe ultraviolet
divergences than its counterpart on the usual commutative plane.
     Finally, we introduce the symmetry transformations of physical states
on noncommutative spaces and discuss them in detail for
     the case of the $E_q(2)$ quantum group.


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