Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-05-20
Phys.Lett. B574 (2003) 111-120
Physics
High Energy Physics
High Energy Physics - Theory
S-matrix formula is revised with proper definition of time-ordering
Scientific paper
10.1016/j.physletb.2003.08.073
In non-commutative field theories conventional wisdom is that the unitarity is non-compatible with the perturbation analysis when time is involved in the non-commutative coordinates. However, as suggested by Bahns et.al. recently, the root of the problem lies in the improper definition of the time-ordered product. In this article, functional formalism of S-matrix is explicitly constructed for the non-commutative $\phi^p$ scalar field theory using the field equation in the Heisenberg picture and proper definition of time-ordering. This S-matrix is manifestly unitary. Using the free spectral (Wightmann) function as the free field propagator, we demonstrate the perturbation obeys the unitarity, and present the exact two particle scattering amplitude for 1+1 dimensional non-commutative nonlinear Schr\"odinger model.
Rim Chaiho
Yee Jae Hyung
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