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arXiv:quant-ph/9908088 · Physical Review A

Comment on “Validity of Feynman’s prescription of disregarding the Pauli principle in intermediate states”

R. M. Cavalcanti

Published Jun 8, 2000• 3 citations
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Abstract

In a recent paper, Coutinho, Nogami, and Tomio [Phys. Rev. A 59, 2624 (1999)] presented an example in which, they claim, Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory fails. We show that, contrary to their claim, Feynman's prescription is consistent with the exact solution of their example.

DOI
10.1103/physreva.62.016101

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Reply to “Comment on ‘Validity of Feynman’s prescription of disregarding the Pauli principle in intermediate states’ ”

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In a recent paper, we raised a question on the validity of Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory. In the preceding Comment, Cavalcanti correctly pointed out that Feynman's prescription is consistent with the exact solution of the model that we used. This means that the Pauli principle does not necessarily apply to intermediate states. We discuss implications of this puzzling aspect.

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Kent Replies:

Adrian Kent

It was pointed out recently [A. Kent, Phys. Rev. Lett. 78 (1997) 2874] that the consistent histories approach allows contrary inferences to be made from the same data. These inferences correspond to projections $P$ and $Q$, belonging to different consistent sets, with the properties that $PQ = QP = 0$ and $P \neq 1 -Q$. To many, this seems undesirable in a theory of physical inferences. It also raises a specific problem for the consistent histories formalism, since that formalism is set up so as to eliminate contradictory inferences, i.e. inferences $P$ and $Q$ where $P = 1 - Q$. Yet there seems to be no sensible physical distinction between contradictory and contrary inferences. It seems particularly hard to defend the asymmetry, since (i) there is a well-defined quantum histories formalisms which admits both contradictory and contrary inferences, and (ii) there is also a well-defined formalism, based on ordered consistent sets of histories, which excludes both. In a recent comment, Griffiths and Hartle, while accepting the validity of the examples given in the above paper, restate their own preference for the consistent histories formalism. As this brief reply explains, in so doing, they fail to address the arguments made against their approach to quantum theory.

arXiv:gr-qc/9808016•Physical Review Letters•Aug 31, 1998•30 citations

Comment on: “Complete resolution of the quantum Zeno paradox for outside observers” [Phys. Lett. A 326 (2004) 32]

Sascha Wallentowitz, P. E. Toschek

Physics Letters A•Mar 15, 2006•1 citation
In a recent paper, Coutinho, Nogami, and Tomio [Phys. Rev. A 59, 2624 (1999)] presented an example in which, they claim, Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory fails. We show that, contrary to their claim, Feynman's prescription is consistent with the exact solution of their example.
Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli's exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingenious trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman's prescription fails. This casts doubts on the general validity of Feynman's prescription.
It was pointed out recently [A. Kent, Phys. Rev. Lett. 78 (1997) 2874] that the consistent histories approach allows contrary inferences to be made from the same data. These inferences correspond to projections PPP and QQQ, belonging to different consistent sets, with the properties that PQ=QP=0PQ = QP = 0PQ=QP=0 and P≠1−QP \neq 1 -QP=1−Q. To many, this seems undesirable in a theory of physical inferences. It also raises a specific problem for the consistent histories formalism, since that formalism is set up so as to eliminate contradictory inferences, i.e. inferences PPP and QQQ where P=1−QP = 1 - QP=1−Q. Yet there seems to be no sensible physical distinction between contradictory and contrary inferences. It seems particularly hard to defend the asymmetry, since (i) there is a well-defined quantum histories formalisms which admits both contradictory and contrary inferences, and (ii) there is also a well-defined formalism, based on ordered consistent sets of histories, which excludes both. In a recent comment, Griffiths and Hartle, while accepting the validity of the examples given in the above paper, restate their own preference for the consistent histories formalism. As this brief reply explains, in so doing, they fail to address the arguments made against their approach to quantum theory.