An Analyst’s Take on Gauge Theory †
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
†
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 42; https://doi.org/10.3390/proceedings2010042
Published: 3 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
We work with a pair of complex-valued scalar fields over a 4-manifold. Our object of study is a first-order Hermitian sesquilinear form, i.e., an integral over the manifold whose integrand is a linear combination of terms “product of gradient of scalar field and scalar field” and “product of two scalar fields”, with complex conjugation in the appropriate places.
We call two sesquilinear forms equivalent if one is obtained from the other by some x-dependent GL (2,C) transformation, i.e., by a change of basis in the infinite-dimensional vector space of pairs of complex-valued scalar fields. Our aim is to provide an explicit description of equivalence classes of sesquilinear forms. We achieve this aim, and in doing this we show that our sesquilinear forms implicitly contain geometric constructs such as Lorentzian metric, connection coefficients and electromagnetic covector potential.
The talk is based on doi:10.1088/1751-8113/48/16/165203 and arXiv:1611.08297 (to appear in JMP).
Conflicts of Interest
The authors declare no conflict of interest.
© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Vassiliev, D. An Analyst’s Take on Gauge Theory. Proceedings 2018, 2, 42. https://doi.org/10.3390/proceedings2010042
AMA Style
Vassiliev D. An Analyst’s Take on Gauge Theory. Proceedings. 2018; 2(1):42. https://doi.org/10.3390/proceedings2010042
Chicago/Turabian StyleVassiliev, Dmitri. 2018. "An Analyst’s Take on Gauge Theory" Proceedings 2, no. 1: 42. https://doi.org/10.3390/proceedings2010042
