Computational method for the retarded potential in the real-time simulation of quantum electrodynamics

• Published in: International journal of quantum chemistry Vol. 116; no. 12; pp. 932 - 938
• Main Authors: Fukuda, Masahiro, Naito, Kento, Ichikawa, Kazuhide, Tachibana, Akitomo
• Format: Journal Article
• Language: English; French; German
• Published: Hoboken Blackwell Publishing Ltd 15.06.2016; Wiley Subscription Services, Inc
• Subjects: Chemistry; DE formula; nonperturbative techniques in quantum field theory; Physical chemistry; quantum electrodynamics; Quantum physics; real-time simulation of quantum field theory; retarded potential
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.25103

We discuss the method to compute the integrals, which appear in the retarded potential term for a real‐time simulation based on quantum electrodynamics. We show that the oscillatory integrals over the infinite interval involved in them can be efficiently performed by the method developed by Ooura and Mori based on the double exponential formula. © 2016 Wiley Periodicals, Inc. Electromagnetic interactions are not transmitted instantaneously. They travel with a finite speed, which equals the speed of light. This is common in relativistic field theory and quantum electrodynamics is no exception. This effect is encapsulated in the retarded potential, where contributions in past time are integrated over consistently with the finite speed of the interaction. This article discusses a method to perform such a complicated integration efficiently.