What are the possible applications of position-space representations of propagators? I'm speaking not only of the well-known free field case, but also of the particles in external fields and/or curved space-time. What might be the possible advantages to have such explicit position-space analytic formulas? What insights these formulas might give?
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1$\begingroup$ Linked. Further see WP. $\endgroup$– Cosmas ZachosCommented Jun 10, 2021 at 19:36
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$\begingroup$ A huge subject/cottage-industry. Decent review: Skenderis, K. (2002). Lecture notes on holographic renormalization. Classical and Quantum Gravity 19 (22), 5849. $\endgroup$– Cosmas ZachosCommented Jun 10, 2021 at 19:48
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$\begingroup$ Well, in the linked topic there is only a discussion of advantages of momentum-space representation, which is obvious. I'm interested in justifying the need to study position-space representations. $\endgroup$– stanislav-iablokovCommented Jun 12, 2021 at 8:30
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