Abstract

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.

Highlights

  • Out in [11] that the vanishing of the amplitudes is consistent with the asymptotic symmetry of QED

  • We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states

  • We discuss the relation between the dressed state formalism and the asymptotic symmetry for QED

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Summary

Review of a problem of S-matrix in QED and the dressed state formalism

Where we have introduced an arbitrary finite time ts at which the Schrodinger operators are defined. There is a way to define an IR finite S matrix It is called the dressed state formalism [3–. Where the superscript s denotes that operators are in the Schrodinger picture, and H0s is the usual free Hamiltonian for QED. B† (and d†) are creation operators of the charged particles (and antiparticles).1 This current is “classical” in the sense that it is a diagonal operator on the usual Fock space. The factors play a similar role as summing the contributions of soft photons, and the S-matrix on HF K is known to be IR finite [3],if we impose the physical state condition. In subsection 5.1, we will comment on a subtlety of the proof of IR finiteness in [3]

Our method and the differences from Faddeev and Kulish’s
Necessity of dresses
Physical states in the Schrodinger picture
Gauge invariant asymptotic states
Interpretation of the Faddeev-Kulish dresses
Coulomb potential by point charges in the asymptotic region
Asymptotic symmetry in the dressed state formalism
Conclusion and further discussion
Softness of dresses
Other future directions

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