QED as a many-body theory of worldlines. II. All-order S -matrix formalism

Feal, Xabier; Tarasov, Andrey; Venugopalan, Raju

doi:10.1103/PhysRevD.107.096021

Title: QED as a many-body theory of worldlines. II. All-order $S$ -matrix formalism

Journal Article · Fri May 26 00:00:00 EDT 2023 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.107.096021· OSTI ID:1975431

; Tarasov, Andrey;

Previously, we developed a first-quantized worldline formalism for all-order computations of amplitudes in QED. In particular, we demonstrated in this framework an all-order proof of the infrared safety of the Faddeev-Kulish (FK) S-matrix for virtual exchanges in the scattering of charged fermions. In this work, we extend the worldline formalism for both the Dyson and FK S-matrix to consider further the emission and absorption of arbitrary numbers of photons. We show how Low’s theorem follows in this framework and derive Weinberg’s theorem for the exponentiation of IR divergences. In particular, we extend our all-order proof of the IR safety of the FK S-matrix to both virtual exchanges and real photon emissions. We argue that the worldline approach leads to a modern Wilsonian interpretation of the IR safety of the FK S-matrix and provides a novel template for the treatment of IR divergences in real-time problems. Using Grassmannian integration methods, we derive a simple and powerful result for N-th rank vacuum polarization tensors. Applications of these methods will be discussed in follow-up work.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704; SC0020081

OSTI ID:: 1975431

Alternate ID(s):: OSTI ID: 1985797

Report Number(s):: BNL-224497-2023-JAAM; PRVDAQ; 096021

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Vol. 107 Journal Issue: 9; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: QED as a many-body theory of worldlines. II. All-order S -matrix formalism

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