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The different forms of Hamiltonian for the coupled system consisting of the electromagnetic field and a non-relativistic charged particle are considered in the context of gauge-transformation theory. The conventional Lagrangian of the system in an arbitrary gauge is converted to a new form by transformation to another arbitrary gauge, and a new formulation of the theory is obtained by expressing the new Lagrangian in terms of the initial potentials. Thus different gauge transformations produce different momenta __∏__ conjugate to the initial vector potential __A__ , and hence different forms of Hamiltonian. The transformations that produce the Coulomb-gauge and Power-Zienau-Woolley (P. Z. W.) Hamiltonians are considered in detail. It is shown that __∏__ is transverse in both cases and only the transverse part of __A__ is accordingly involved in the field quantization; neither the longitudinal part of __A__ nor the scalar potential appears explicitly, the instantaneous Coulomb energies being included via an electronic polarization determined by the gauge generator. The transformations between gauges are illustrated by simple diagrammatic representations of __A__ and __∏__ . Comparar

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Publisher

The Royal Society

Published

1983

Language

EN

Field

Physics and Astronomy (Physical Sciences)