Gomis, J; Mehen, T; Wise, MB, *Quantum field theories with compact non-commutative extra dimensions*,
Journal of High Energy Physics, vol. 4 no. 8 PART B
(2000),
pp. 1-15 .
**Abstract:**

*We study field theories on spaces with additional compact noncommutative dimensions. As an example, we study φ3 on ℝ1,3xdouble-struck T signθ2 using perturbation theory. The infrared divergences in the non-compact theory give rise to unusual dynamics for the mode of φ 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.*