/ 99 08 08 8 v 1 31 A ug 1 99 9 Comment on “ Validity of Feynman ’ s prescription of disregarding the Pauli principle in intermediate states ”

Feynman’s prescription of disregarding the exclusion principle in intermediate states of perturbation theory is based in his observation [1] that all virtual processes that violate that principle (formally) cancel out order by order in perturbation theory. However, Coutinho, Nogami and Tomio have recently presented an example [2] in which Feynman’s prescription seems to fail. They calculated (in second order perturbation theory) the energy shift W ≡ E(λ)−E(0) of the ground state of the one-particle sector of the one-dimensional bag-model caused by the potential V (x) = λx. The calculation was performed using both prescriptions, i.e., either excluding virtual transitions to occupied states, in accordance with the Pauli principle (method I), or including such transitions, as suggested by Feynman (method II). It turns out that the result depends on the prescription used; in the massless case, for instance, WI 6= 0 and WII = 0. In view of this discrepancy, Coutinho et al. suggested that one should abandon Feynman’s prescription and remain faithful to the Pauli principle in every step of the calculation. The purpose of this Comment is to show that the opposite alternative is the correct one. More precisely, we show that WII agrees (while WI does not) with the exact value of W in the massless case. To calculate W we need to solve the Dirac equation