By L. C. Biedenharn
This article develops the speculation of angular momentum from the perspective of a basic symmetry in nature and exhibits how this idea pertains to utilized parts of study in smooth quantum physics.
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Notice however that t′ (or rather 4t′) is different from the polaronic bandwidth and it does not represent the exponentially suppressed polaronic hopping. Indeed, a hole is no longer a good excitation but carries a consistent cloud of phonons with intrinsic dynamics and finite spatial extension. In the adiabatic regime, the lattice relaxation is very slow and the electrons on a short timescale are delocalized. As a result, the ARPES signal follows the non-renormalized frozen lattice bands and t′ ≈ t.
As a result, the itineracy of the single particle excitations depends substantially on the timescale of the probe. A fast probe, like photoemission, produces single particle states that “feel” the frozen lattice dispersion. At the opposite limit, an adiabatic perturbation would generate a response that can be described in terms of heavy quasiparticles dispersing along narrow polaronic bands. In a rigorous treatment of the electronic response, one would calculate exactly the single particle propagator.
Angular momentum in quantum physics: theory and application by L. C. Biedenharn