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I suppose that a general definition of the twist remove normalization for a functional Φ is given by the condition: ∫Dχ Φ[χ]^{*} Φ[χ] = 1, (d/dε) ∫Dχ Φ[χ]^{*} Φ[χ(□  ε)] _{ε = 0} = 0, where χ(□  ε) is a function such that [χ(□  ε)](t) = χ(t  ε) for all t. Possibly, a general definition of the twist remove normalization for a functional Φ is given by the condition: ∫Dχ Φ[χ]^{*} Φ[χ] = 1, lim_{ε → 0} ∫Dχ Φ[χ]^{*} Φ[χ(□  ε)] = 1 because the phase factor exp[⊿t(i/h)＜jH]j＞] in Problems in Grammatical Physics > Quantum Field Theory on the TimeAxis > Quadratic Formula(not backed up) corresponds not to (d/dε) ∫Dχ Φ[χ]^{*} Φ[χ(□  ε)] _{ε = 0} but to lim_{ε → 0} ∫Dχ Φ[χ]^{*} Φ[χ(□  ε)]. Possibly, the twist remove normalization may not be necessary for Φ in the case that we use exp∫dt instead of Π_{t}. When Φ[χ] = Σ_{j} Π_{k} φ_{j}(χ(k/α), k/α), change of the phase factor of φ_{j} φ'_{j}(χ(k/α), k/α) = exp[iF_{j}(k/α)]φ_{j}(χ(k/α), k/α) changes only the whole phase factor by exp[iΣ_{k}F_{j}(k/α)]. Different paterns of changing phase factors without changing the whole phase factor can not be distinguished. This concerns the energy ambiguity problem.  This article is a rewrite of the article 'Twist Remove Normalization' in the following page. Later Edition@Theory of Quantum History Entangled in Timelike Direction@Products of Grammatical Physics@Grammatical Physics@Forum@Vintage(20082014) The content of this article was presented by me at JPS 2013 Autumn Meeting. 

Author Yuichi Uda, Write start at 2015/05/21/20:15JST, Last edit at 2015/05/23/20:05JST  






