The dressed state formalism enables us to define the infrared finite S-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss’s law naturally leads to proper asymptotic states for the infrared finite S-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.

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Published in Journal of High Energy Physics, v. 2019, issue 6, article 23, p. 1-22.

© The Author(s) 2019

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Article funded by SCOAP3.

The work of SS is supported in part by the Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows No.16J01004.

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