# PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism

PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being $$iA_{\mu }$$ i A μ rather than $$A_{\mu }$$ A μ itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Foundations of Physics Springer Journals

# PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism

, Volume 47 (9) – May 9, 2016
29 pages

/lp/springer_journal/pt-symmetry-conformal-symmetry-and-the-metrication-of-electromagnetism-3Kcd5itAqd
Publisher
Springer Journals
Subject
Physics; History and Philosophical Foundations of Physics; Quantum Physics; Classical and Quantum Gravitation, Relativity Theory; Statistical Physics and Dynamical Systems; Classical Mechanics; Philosophy of Science
ISSN
0015-9018
eISSN
1572-9516
D.O.I.
10.1007/s10701-016-0017-8
Publisher site
See Article on Publisher Site

### Abstract

We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being $$iA_{\mu }$$ i A μ rather than $$A_{\mu }$$ A μ itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.

### Journal

Foundations of PhysicsSpringer Journals

Published: May 9, 2016

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