Abstract
In this paper we give a sense to the distributional multiplicative product \((\delta (x_o - \left| x \right|)/\left| x \right|^{(n - 2)/2} )(\delta (x_o + \left| x \right|)/\left| x \right|^{(n - 2)/2} )\). For the case n=4 we obtain a formula which is used for a perturbative calculation of Green function in quantum field theories. As an application of our product, we show the calculation of the self-energy of the theory of \(\lambda \emptyset ^4 \).
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References
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C. Bollini and M. Rocca, Convolution of ultradistributions, Preprint, La Plata (1997, in preparation).
I.M. Gelfand and G.E. Shilov, Generalized Functions, Vol. 1 (Academic Press, New York, 1964).
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Aguirre Téllez, M. The multiplicative product \((\delta (x_0 - \left| x \right|)/\left| x \right|^{(n - 2)/2} )(\delta (x_0 + \left| x \right|)/\left| x \right|^{(n - 2)/2} )\) . Journal of Mathematical Chemistry 22, 149–160 (1997). https://doi.org/10.1023/A:1019128015266
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DOI: https://doi.org/10.1023/A:1019128015266