Computer simulations for the scattering of a relativistic wave packet by a step potential are performed. Under the condition of the Klein paradox, where the height of the potential barrier becomes supercritical, the scattering induces the creation of electron–positron pairs. The “pair creation” is demonstrated in the present simulation by making use of the hole theory.

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It is shown that the operator formulation of the quantization of dynamical systems subject to second class constraints by Batalin and Fradkin (BF method) is equivalent to the projection-operator method (POM), which is the alternative method of the quantization of such systems, at the commutator level. It is also shown that the commutators in the BF method as well as those in the POM contain a quantum effect, which is completely missed in the usual quantization scheme with the Dirac brackets.

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