Transition amplitudes and sewing properties for bosons on the Riemann sphere

Details Transition amplitudes and sewing properties for bosons on the Riemann sphere Transition amplitudes and sewing properties for bosons on the Riemann sphere

2006-12-21

arxiv.org/abs/math-ph/0612072v1

Physics

Mathematical Physics

33 pages

Scientific paper

10.1063/1.2740468

We consider scalar quantum fields on the sphere, both massive and massless. In the massive case we show that the correlation functions define amplitudes which are trace class operators between tensor products of a fixed Hilbert space. We also establish certain sewing properties between these operators. In the massless case we consider exponential fields and have a conformal field theory. In this case the amplitudes are only bilinear forms but still we establish sewing properties. Our results are obtained in a functional integral framework.

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