Quantization via hopping amplitudes: Schrödinger equation and free QED
نویسنده
چکیده
Schrödinger’s equation with scalar and vector potentials is shown to describe “nothing but” hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field. The main point of the argument is the superposition principle for state vectors; Lagrangians, path integrals, or classical Hamiltonians are not (!) required. Analogously, the Hamiltonian of the free electromagnetic field is obtained as a twofold continuum limit of unitary hopping in Z(N) link configuration space, if gauge invariance and C and P symmetries are imposed. PACS: 03.65.Bz,03.70.+k,11.15.Ha
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