**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Thu, 5 Aug 1999 09:55:17 +0300 (EET DST)*

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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

hep-th/9904132

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.

Best,

MP

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