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Maxwell’s displacement current turns out to be a topological current: the commuting of space and time derivatives of the electric field gives a conservation law whose charge density is the divergence of E. A parallel plate capacitor shows it at work.
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The phase behind Young’s double slit interference, for both non-relativistic particles and light, turns out to be the geometric phase, traceable to Feynman’s rule of adding amplitudes over mutually exclusive routes.
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Using the sl(2,R) algebra present in the system, the two dimensional nonlinear Schrödinger equation is shown to admit infinitely many conserved charges in involution, establishing its Liouville integrability.
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A two-dimensional gas of particles with repulsive contact interactions can be mapped exactly onto free particles, and with a harmonic trap onto decoupled oscillators. The sl(2,R) algebra is the key to both maps.
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This is my first post on this blog, and I welcome you all. May the force be with all of us !
