Abstract
A unitary transformation on the total Hamiltonian of quantum electrodynamics is shown to relate the length and velocity forms of both nonrelativistic and relativistic oscillator strengths. For the gauge-violating self-consistant Hamiltonian of the Hartree-Fock approximation, the conventional relation between length and velocity forms is an approximation to a general relation between interaction Hamiltonians connected by the unitary transformation. From the point of view of the unitary transformation, the velocity form is as reliable as the length form, and the forms of length formulas of relativistic and nonrelativistic oscillator strengths are identical.
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