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Gauge independence of the eikonal equation in Yang-Mills gravity

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Abstract

When one takes the geometric-optics limit of Maxwell’s wave equations in Yang-Mills gravity, one arrives at a new eikonal equation. Although we cannot perform the usual electromagnetic gauge transformation to the eikonal equation, we have the same equation for a wide class of gauge conditions, including the non-covariant temporal and axial gauges. We also show the presence of a small correction term if the large frequency limit is not taken. This small term suggests a frequency dependence in the deflection of light experiment. Moreover, there is a small violation of the electromagnetic U 1 gauge symmetry by gravity. This violation is crucial for the emergence of an effective Riemannian metric tensor associated with the new eikonal equation in Yang-Mills gravity. The results are consistent with known experiments and more accurate experiments in the future are required to test them.

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Authors and Affiliations

  1. Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, MA, 02747-2300, USA

    Kazuo Ota Cottrell & Jong-Ping Hsu

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  1. Kazuo Ota Cottrell
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  2. Jong-Ping Hsu
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Correspondence to Kazuo Ota Cottrell.

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Cottrell, K.O., Hsu, JP. Gauge independence of the eikonal equation in Yang-Mills gravity. Eur. Phys. J. Plus 130, 147 (2015). https://doi.org/10.1140/epjp/i2015-15147-8

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  • DOI: https://doi.org/10.1140/epjp/i2015-15147-8

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