Asymptotic symmetries of QED and Weinberg's soft photon theorem (1505.05346v1)

Abstract: Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.

• The paper extends Weinberg’s soft photon theorem to include massive scalar particles, bridging large gauge transformations and asymptotic symmetries.
• It introduces a new manifold-based phase space at time-like infinity, redefining charge calculations in QED.
• The findings link Ward identities with soft photon emissions, offering valuable insights for quantum gravity and infrared behavior in scattering processes.

Analyzing Asymptotic Symmetries in Quantum Electrodynamics

The paper authored by Miguel Campiglia and Alok Laddha addresses an intricate aspect of Quantum Electrodynamics (QED), closely examining the asymptotic symmetries connected to Weinberg’s soft photon theorem. The focus of the research is on removing the limitation of considering only massless particles, thus expanding the theoretical framework to include massive charged scalar particles within a QED context. This paper sits at the intersection of advanced theoretical physics and mathematics, primarily dealing with symmetries, scattering amplitudes, and the rich structure of phase spaces at the asymptotic boundaries of spacetime.

Expansion Beyond Massless Particles

The authors meticulously extend the considerations of previous studies by elaborating on the compatibility between large gauge transformations in QED and Weinberg’s soft photon theorem within the framework of massive scalar fields. This extension is nontrivial as it involves reformulating how asymptotic phase spaces are defined at time-like infinity for massive fields rather than defaulting to the null infinity applicable to massless scenarios.

New Phase Space Conceptions

The theoretical underpinning of this paper is significantly enriched by the introduction of a new manifold-based description at time-like infinity, akin to the already established phase space associated with massless fields at null infinity. This approach is critical for predicting and justifying the presence of large gauge symmetries within scalar QED involving massive particles. The noteworthy implication here is that the large gauge transformations underpinning these symmetries do not diminish at these infinities, fundamentally impacting how charges are defined and how they can be equivalently related to soft theorems.

Bridging Large Gauge Transformations and Soft Theorems

A pivotal result of the paper confirms the equivalence between the derived Ward identities, associated with these large gauge transformations, and Weinberg’s soft photon theorem within the scalar QED setting. The intricacy of this equivalence lies in its demonstration that softly emanated photons during scattering processes—previously perceived independent of such identity transformations—are indeed correlated via infrared constraints imposed by asymptotic symmetries.

Methodological Approach & Results

• Gauge Choice: The choice of the Lorenz gauge significantly facilitates delineating the equivalences between soft theorems and Ward identities. This gauge ensures a consistent extension of symmetries at both null and time-like infinities.
• Numerical Results: Specific calculations bolster the claims, showing how the theoretical constructs align with anticipated behavior of asymptotic fields and the associated soft factors.

Implications for Quantum Gravity

The theoretical underpinning provided in this paper has broader implications, particularly concerning the symmetry groups in quantum gravity. By showing that the group of large gauge transformations exerting symmetries on massive fields retains equivalency with soft photon theorems, a foundation is set for exploring similar symmetry-theorem relationships in quantum gravity interactions, particularly those involving massive and massless gravitating particles in asymptotically flat spacetime.

Future Directions

Further research could explore the intricacies of these newly conceived phase spaces and how they might align with well-established structures like the BMS group in gravitational interactions. Additionally, examining the quantum implications might provide further insights into coherent states and the infrared behavior of the S-matrix in futuristic iterations of QED and quantum gravity.

In summary, Campiglia and Laddha's work provides a sophisticated and rigorous exploration of asymptotic symmetries in QED, effectively bridging gaps in current understanding concerning the interactions involving massive fields and opening the pathway to broader theoretical applications in modern quantum theory.