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arXiv · 1104.1629

Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane

A. P. Balachandran·Pramod Padmanabhan·Amilcar R. de Queiroz
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Abstract

Field theories on the Groenewold-Moyal(GM) plane are studied using the Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields is treated in detail. The S-matrix elements in this non-perturbative approach are shown to be equal to the interaction representation S-matrix elements. This is a new non-trivial result: in both cases, the S-operator is independent of the noncommutative deformation parameter $\theta_{\mu\nu}$ and the change in scattering amplitudes due to noncommutativity is just a time delay. This result is verified in two different ways. But the off-shell Green's functions do depend on $\theta_{\mu\nu}$. In the course of this analysis, unitarity of the non-perturbative S-matrix is proved as well.

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A. P. Balachandran, Pramod Padmanabhan, Amilcar R. de Queiroz. 2011-04-08. Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane. https://doi.org/10.1103/physrevd.84.065020

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