Gomis, J; Mehen, T; Wise, MB, *Quantum Field Theories with Compact Noncommutative Extra Dimensions*,
JHEP, vol. 8 no. 8 PART B
(2000),
pp. 29 .
**Abstract:**

*We study field theories on spaces with additional compact
noncommutative dimensions. As an example, we study \phi^3 on
R^{1,3}\times T^{2}_\theta using perturbation theory. The
infrared divergences in the noncompact theory give rise to
unusual dynamics for the mode of \phi which is constant
along the torus. Correlation functions involving this mode
vanish. Moreover, we show that the spectrum of Kaluza-Klein
excitations can be very different from the analogous
commuting theory. There is an additional contribution to the
Kaluza-Klein mass formula that resembles the contribution of
winding states in string theory. We also consider the effect
of noncommutativity on the four dimensional Kaluza-Klein
excitations of a six dimensional gauge field.*