Abstract
We provide a unified geometrical origin for both boundary charges and particle dressings, with a focus on electrodynamics. The method is furthermore generalizable to QCD and gravity, and can be extended to the non-perturbative domain.
Highlights
Geometrical tools often give valuable insight into physical questions
Their flows generate gauge orbits in ΦYM, which can be interpreted as the fibers of an infinitedimensional principal fiber bundle G ↪ ΦYM→π 1⁄2ΦYM, where 1⁄2ΦYM ≔ ΦYM=G is the reduced space of physical field configurations
These definitions are in complete analogy with the finitedimensional principal fiber bundle picture of gauge theory; see, e.g., Ref. [17]
Summary
Geometrical tools often give valuable insight into physical questions. Examples abound: from the role of Riemannian geometry in general relativity, to the use of the Atiyah-Singer index theorem in studying anomalies in quantum field theories, with many examples in between, before, and more recently. Beyond being a mere mathematical curiosity, this tool is surprisingly powerful, both in the study of boundary charges and in the characterization of the dressings of charged particles in gauge theories These two topics—boundary charges and dressings— were related by Bagan et al [2], upon defining constituent quarks as color-charged gauge-invariant entities. Summary of results.—After introducing concepts and notation for dealing efficiently with the geometry of field space, we will show how a simple choice of π, naturally related to the dynamics of a gauge theory, readily provides a notion of dressing. This is found to coincide with the Dirac dressing in the context of 3 þ 1 electrodynamics. Further results and explicit examples of field-space connections will appear in a forthcoming publication [15]
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