Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s second theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.
Avery, Steven G. and Schwab, Burkhard U. W.. "Noether’s second theorem and Ward identities for gauge symmetries." Journal of High Energy Physics (Online), vol. 2016, no. 2, Feb. 2016. https://doi.org/10.1007/JHEP02(2016)031
Avery, Steven G., & Schwab, Burkhard U. W. (2016). Noether’s second theorem and Ward identities for gauge symmetries. Journal of High Energy Physics (Online), 2016(2). https://doi.org/10.1007/JHEP02(2016)031
Avery, Steven G., and Schwab, Burkhard U. W., "Noether’s second theorem and Ward identities for gauge symmetries," Journal of High Energy Physics (Online) 2016, no. 2 (2016), https://doi.org/10.1007/JHEP02(2016)031
@article{osti_1327284,
author = {Avery, Steven G. and Schwab, Burkhard U. W.},
title = {Noether’s second theorem and Ward identities for gauge symmetries},
annote = {Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s second theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.},
doi = {10.1007/JHEP02(2016)031},
url = {https://www.osti.gov/biblio/1327284},
journal = {Journal of High Energy Physics (Online)},
issn = {ISSN 1029-8479},
number = {2},
volume = {2016},
place = {United States},
publisher = {Springer Berlin},
year = {2016},
month = {02}}
Bondi, Hermann; Van der Burg, M. G. J.; Metzner, A. W. K.
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 269, Issue 1336, p. 21-52https://doi.org/10.1098/rspa.1962.0161
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 270, Issue 1340, p. 103-126https://doi.org/10.1098/rspa.1962.0206