Remarks on time-space noncommutative field theories

Abstract

We propose a physical interpretation of the perturbative breakdown of unitarity in timelike noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closedstring modes. In this way, we give a unified view of the string-theoretical and the fieldtheoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.

General properties of non-commutative field theories

“…θ i0 = 0. In this case, however, non-locality is accompanied by a breakdown of unitarity reflected in the fact that the optical theorem is not satisfied [29,30]. In addition there is no well-defined…”

“…Actually, the optical theorem can be formally restored by taking into account the interchange of undecoupled string states in intermediate channels, although they are both tachyonic and have negative norm [30].…”

Schwinger model in noncommutating space–time

“…A contentious issue in this scenario is the aspect of noncommutativity in the time-space sector. It was argued that introduction of space-time noncommutativity spoils unitarity [3,4] or even causality [5]. However, much attention has been devoted in recent times to circumvent these difficulties in formulating theories with θ 0i = 0 [6,7,8].…”

Noncommutative Field Theories and (Super)string Field Theories

“…One starts with the N-point diagram: It was proved that the amplitude (5.61) can be presented in CFT language as 62) where the correlation functions must be calculated on a surface R (the so-called string scattering configuration). For Witten's vertex the surface R looks like it is sketched in Figure 12.…”