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How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations

Francesco Caravaglios
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Abstract

Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of epsilon =n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/epsilon and the finite part.

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Francesco Caravaglios. 2000-04-04. How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations. https://doi.org/10.1016/s0550-3213(00)00391-6

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