Riassunto analitico
In the present study we investigate a locally supersymmetric worldline action on the line, i.e. 1D supergravity, show that it describes a spin 1/2 particle, and compute the master formula that describes the N-photon amplitude. While the same computation for the scalar particle, both in an abelian and nonabelian background, has already been worked out in detail, the computation for the spinning particle has been performed with the aid of spin factors introduced by Feynman and a “symbol map" that allows converting certain anticommuting objects into products of gamma matrices. The scope of this work is to fill this gap and obtain the general N-photon amplitude with a pure worldline approach. In this approach, coherent states are employed, and it is of primary importance to write the result in terms of gamma matrices. By doing so, a map between coherent states and gamma matrices is constructed, and which turns out to be vaguely reminiscent of the symbol map.
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Abstract
In the present study we investigate a locally supersymmetric worldline action on the line, i.e. 1D supergravity, show that it describes a spin 1/2 particle, and compute the master formula that describes the N-photon amplitude. While the same computation for the scalar particle, both in an abelian and nonabelian background, has already been worked out in detail, the computation for the spinning particle has been performed with the aid of spin factors introduced by Feynman and a “symbol map" that allows converting certain anticommuting objects into products of gamma matrices. The scope of this work is to fill this gap and obtain the general N- photon amplitude with a pure worldline approach. In this approach, coherent states are employed, and it is of primary importance to write the result in terms of gamma matrices. By doing so, a map between coherent states and gamma matrices is constructed, and which turns out to be vaguely reminiscent of the symbol map.
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