Quantum fields with noncommutative target spaces

Quantum field theories (QFT’s) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT’s with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [ R. Oeckl Commun. Math. Phys. 217 451 (2001)], and others [ A. P. Balachandran, G. Mangano, A. Pinzul and S. Vaidya Int. J. Mod. Phys. A 21 3111 (2006); A. P. Balachandran, A. Pinzul and B. A. Qureshi Phys. Lett. B 634 434 (2006); A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, arXiv:hep-th/0608138; A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi and S. Vaidya Phys. Rev. D 75 045009 (2007); A. Pinzul Int. J. Mod. Phys. A 20 6268 (2005); G. Fiore and J. Wess Phys. Rev. D 75 105022 (2007); Y. Sasai and N. Sasakura Prog. Theor. Phys. 118 785 (2007)]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al. [ J. M. Carmona, J. L. Cortes, J. Gamboa and F. Mendez Phys. Lett. B 565 222 (2003); J. M. Carmona, J. L. Cortes, J. Gamboa and F. Mendez J. High Energy Phys. 2003 058 ()]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed blackbody spectrum, which is analyzed in detail. The difference between the usual and the deformed blackbody spectrum appears in the region of high frequencies. Therefore we expect that the deformed blackbody radiation may potentially be used to compute a Greisen-Zatsepin-Kuzmin cutoff which will depend on the noncommutative parameter θ.