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Part I: Don't Shake That Solenoid Too Hard: Particle Production from Aharonov-Bohm

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Five decades ago, Aharonov and Bohm illustrated the indispensable role of the vector potential in quantum dynamics by showing (theoretically) that scattering electrons around a solenoid, no matter how thin, would give rise to a non-trivial cross section that had a periodic dependence on the product of charge and total magnetic flux. (This periodic dependence is due to the topological nature of the
interaction.) We extend the Aharonov-Bohm analysis to the field theoretic domain: starting with the quantum vacuum (with zero particles) we compute explicitly the rate of production of electrically charged particle-antiparticle pairs induced by shaking a solenoid at some fixed frequency. (This body of work can be found in arXiv: 0911.0682 and 1003.0674.)

Part II: The N-Body Problem in General Relativity from Perturbative QFT

In the second portion of the talk, I will describe how one may use methods usually associated with perturbative quantum field theory to develop what is commonly known as the post-Newtonian program in General Relativity -- the weak field, non-relativistic, gravitational dynamics of compact astrophysical objects. The 2 body aspect of the problem is a large industry by now, driven by the need to model the gravitational waves expected from compact astrophysical binaries. I will discuss my efforts to generalize these calculations to the N-body case. (This work can be found in arXiv: 0812.0012.)