Abstract
An analogy between the removal of nonphysical relative time (or relative energy) in the supersymmetric two-particle problem and the account of local gauge invariance in supersymmetric quantum field theory is discussed. A group of gauge transformations for the Bethe-Salpeter amplitudes is suggested, the invariants of which are the relativistic three-dimensional (quasipotential) wave functions in the Logunov-Tavkhelidze approach. Subsidiary conditions imposed on the Bethe-Salpeter amplitudes in the Todorov approach are shown to be equivalent to appropriate gauge fixing.
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