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Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED

Hayato Hirai, Sotaro Sugishita

TL;DR

The paper investigates memory effects, asymptotic symmetries, and soft theorems in massive QED, showing that electromagnetic memory arises from the conservation of large-gauge charges in Lorenz gauge and deriving leading and subleading memories. It provides a BRST-based argument that large gauge transformations are physical symmetries, and constructs the corresponding soft and hard charges, including for massive scalars, establishing Ward-Takahashi identities that match the leading and subleading soft photon theorems. The work clarifies how memory effects are encoded in asymptotic data and offers explicit operator expressions for subleading charges, illuminating the IR structure of QED with massive charges and setting the stage for extensions to gravity and nonperturbative regimes. Overall, it links classical memory, quantum soft theorems, and asymptotic symmetries in a coherent framework for massive charged systems. Significance lies in formalizing the IR structure of QED beyond massless limits and providing concrete charge constructions that connect observable memory effects to symmetry principles.

Abstract

We present several results on memory effects, asymptotic symmetry and soft theorems in massive QED. We first clarify in what sense the memory effects are interpreted as the charge conservation of the large gauge transformations, and derive the leading and subleading memory effects in classical electromagnetism. We also show that the sub-subleading charges are not conserved without including contributions from the spacelike infinity. Next, we study QED in the BRST formalism and show that parts of large gauge transformations are physical symmetries by justifying that they are not gauge redundancies. Finally, we obtain the expression of charges associated with the subleading soft photon theorem in massive scalar QED.

Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED

TL;DR

The paper investigates memory effects, asymptotic symmetries, and soft theorems in massive QED, showing that electromagnetic memory arises from the conservation of large-gauge charges in Lorenz gauge and deriving leading and subleading memories. It provides a BRST-based argument that large gauge transformations are physical symmetries, and constructs the corresponding soft and hard charges, including for massive scalars, establishing Ward-Takahashi identities that match the leading and subleading soft photon theorems. The work clarifies how memory effects are encoded in asymptotic data and offers explicit operator expressions for subleading charges, illuminating the IR structure of QED with massive charges and setting the stage for extensions to gravity and nonperturbative regimes. Overall, it links classical memory, quantum soft theorems, and asymptotic symmetries in a coherent framework for massive charged systems. Significance lies in formalizing the IR structure of QED beyond massless limits and providing concrete charge constructions that connect observable memory effects to symmetry principles.

Abstract

We present several results on memory effects, asymptotic symmetry and soft theorems in massive QED. We first clarify in what sense the memory effects are interpreted as the charge conservation of the large gauge transformations, and derive the leading and subleading memory effects in classical electromagnetism. We also show that the sub-subleading charges are not conserved without including contributions from the spacelike infinity. Next, we study QED in the BRST formalism and show that parts of large gauge transformations are physical symmetries by justifying that they are not gauge redundancies. Finally, we obtain the expression of charges associated with the subleading soft photon theorem in massive scalar QED.

Paper Structure

This paper contains 19 sections, 162 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. Infinite number of conserved charges
  3. Leading memory effect
  4. Subleading memory effect
  5. Asymptotic symmetry as physical symmetry in QED
  6. Review of the covariant quantization in QED
  7. Asymptotic gauge fields as the physical Cauchy data
  8. Asymptotic gauge fields as the physical Cauchy data
  9. Leading soft photon theorem
  10. Subleading charges in massive QED
  11. Subleading soft photon theorem and the soft part of the subleading charges
  12. Hard part of the subleading charges
  13. Discussions and Outlook
  14. A concrete example
  15. Electromagnetic fields of uniformly moving charges
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The region where we consider the current conservation. The directions along the two sphere $S^2$ are suppressed in this figure. The blue lines represent trajectories of massive charged particles, which scatter at a small region. The red line represents a direction of the radiation emitted from this scattering. The region is parametrized by two parameters $T$ and $U$. The parameter $T$ is so large that all of the given massive particles go through the surface $\Sigma_i$ and $\Sigma_f$, and $U$ is also so large that any radiation coming from the scattering region passes through $\Sigma_+$.