New Symmetries of Massless QED (1407.3789v2)

Abstract: An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large $U(1)$ gauge transformations that asymptotically approach an arbitrary function $\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity ($\mathscr I^+$) but are independent of the retarded time. The value of $\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on $\mathscr I^+$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\varepsilon\neq$ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a $U(1)$ boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

• The paper identifies a new class of U(1) asymptotic symmetries that serve as electromagnetic analogs to gravitational supertranslations.
• It employs asymptotic expansions and canonical transformations at null infinity to derive a Ward identity corresponding to the abelian soft photon theorem.
• The analysis reveals that spontaneous symmetry breaking produces zero-momentum photons, offering fresh insights into soft photon emission and absorption in QED.

An Insightful Overview of "New Symmetries of Massless QED"

The paper "New Symmetries of Massless QED" by Temple He, Prahar Mitra, Achilleas P. Porfyriadis, and Andrew Strominger explores the intriguing domain of asymptotic symmetries in abelian gauge theories, specifically Quantum Electrodynamics (QED) involving massless charged particles. The research advances the understanding of QED by identifying a new class of symmetries that emerge from large U(1) gauge transformations. These symmetries are significant because they persist even as the transformations approach an arbitrary function on the conformal sphere at future null infinity ($\mathcal{I}^+$) and remain constant along the null generators.

The principal assertion of the paper is that these newly identified symmetries can be seen as electromagnetic analogs to the BMS (Bondi-van der Burg-Metzner-Sachs) supertranslations previously noted in gravitational contexts. A remarkable aspect of these symmetries is their spontaneous breaking in the conventional vacuum state of QED, with the corresponding Goldstone modes manifesting as zero-momentum photons, reflecting a unique bosonic mode living on the conformal sphere. This insight not only refines the understanding of soft photon theorems but also provides a unified framework that relates these theorems to underlying symmetry principles, thus offering an essential conceptual leap.

The paper meticulously derives the mathematical framework supporting these conclusions, employing techniques such as the asymptotic expansion at future and past null infinities, large gauge transformations, and canonical formulation. The research demonstrates that the new symmetries entail a Ward identity that corresponds to the abelian soft photon theorem, thereby linking them to observable scattering phenomena.

A critical contribution of this work is the articulation of the matching conditions between initial and final data concerning the conformal compactification of Minkowski spacetime. These conditions yield a canonical phase space description wherein symmetries act as canonical transformations, showcasing the theoretically robust structure of QED at null infinity. Moreover, these considerations lead to the profound realization that the emission and absorption processes of soft photons can be understood via these symmetries, effectively integrating them within the quantum scattering framework.

The authors also discuss the practical intricacies of extending this analysis to scenarios involving stable massive charged particles, acknowledging the technical hurdles presented by real-world QED where electrons are stable.

From a quantum perspective, the paper elucidates the relevance of these symmetries in the quantum field theory context by demonstrating that the quantum Ward identity derived from these symmetries encapsulates the soft photon theorem. This connection underscores the essential role of such symmetries in enhancing the precision of high-energy collider predictions and potentially forms a foundational basis for alternative holographic formulations in quantum gravity arenas.

In conclusion, this paper marks a substantial progression in understanding the nuanced equivalences between soft theorems and asymptotic symmetries. The implications of the new symmetries on both practical computations in QED and theoretical avenues in quantum gravity are profound and promote further exploration into their manifestations and applications. Future developments may involve extending these findings to encompass other gauge theories and interacting systems, potentially unveiling new symmetries and insights that reshape the understanding of quantum field theories at large.