Reformulation of the g shift in metals starting with the Pauli equation

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Abstract
The gauge invariant properties of the Dirac equation are used to define the gauge invariant physical operators in time dependent gauges. The extension to approximate equations is reviewed. In order to match the trial wavefunction with gauge the free particle in a constant magnetic field is examined in the two component approximation. A new gauge, the classical orbit gauge, is introduced and exact wave packet solutions, which follow the classical orbits, are found. These solutions are used to show how the equations of motion can be used as a criterion for a trial wavefunction. For the usual wave packet one obtains the known result of a match with the Jones and Zener gauge (1934). Finally, these results are used to reformulate the theoretical evaluation of the g shift in metals starting with the Pauli equation.

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