Abstract
We examine the moments of the Gaussian integral and relate them to Feynman diagrams. We next introduce a quartic term and show how it leads to a seemingly paradoxical result. The article is addressed to the novice, but we believe that it may also serve as an opening lecture on the topic of Feynman diagrams.
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Suggested Reading
Richard P Feynman, The Theory of Positrons Physical Review, Vol.76, pp.749–761, 1949.
Richard D Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, New York: Dover Books, 1992.
A Zee, Quantum Field Theory in a Nutshell, Second Edition, New Jersey: Princeton University Press, 2010.
See Carl M Bender and Steven A Orszag, Advanced Mathematical Methods for Scientists and Engineers, New York: McGraw-Hill, 1978.
Acknowledgment
Raghu Mahajan is supported by US Department of Energy grant number DE-SC0016244. Vijay A. Singh acknowledges support from the Raja Ramanna Fellowship by the DAE.
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Raghu Mahajan completed his PhD from Stanford University in 2017 and is currently a postdoctoral fellow at Princeton University. He topped the IIT-JEE entrance exam in 2006 and won a gold medal at the International Physics Olympiad held in Singapore, 2006.
Vijay A Singh is a Raja Ramana Fellow at the Centre for Excellence in Basic Sciences. He was the National Coordinator of the Science Olympiad programme and the National Initiative on Undergraduate Sciences for about a decade at HBCSE (TIFR). Earlier he taught for twenty years at IIT Kanpur.
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Mahajan, R., Singh, V.A. Feynman Diagrams: A Toy Example. Reson 24, 653–659 (2019). https://doi.org/10.1007/s12045-019-0823-3
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DOI: https://doi.org/10.1007/s12045-019-0823-3