Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
The geometry underlying electromagnetism
Presented by Mario Serna (Department of Physics, United States Air Force Academy)
Geometry is often characterized by dragging a vector in as parallel a manner as possible along a closed path. The mathematical definition of curvature is proportional to the angle change in such a vector after transport around the loop. This is the curvature used in General Relativity. This talk will explain how curvature relates to E&M. In quantum mechanics, the Aharonov-Bohm effect shows us that the vector potential (A) for E&M is more fundamental than the electric and magnetic fields. In the Aharanov-Bohm effect, a wave function that travels around both sides of a region with a magnetic field undergoes a phase shift proportional the enclosed magnetic field. The angle difference in the Aharonov-Bohm effect is a result of the same type of geometry described by parallel transporting vectors around a loop. In this talk, I will show three superficially different schools for manifesting this geometry to represent E&M. I will describe how to make rigorous the 'ings' used by Brian Green to depict Kaluza-Klein theory. I will describe how to visualize curvature of E&M fields with Grassmanians using a technique developed with Prof Cahill in the 2000s. Last, I will connect these representations to work done at MIT on a hidden spatial geometry of Yang-Mills theory of which E&M is a special case.
The topic based on http://arxiv.org/abs/1308.1092
2:00 pm, Tuesday, March 25, 2014
PAIS-2540, PAIS
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