since 2006
Help Sitemap
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,
limε → 0 ∫Dχ Φ[χ]* Φ[χ(□ - ε)] = 1
because the phase factor exp[-⊿t(i/h)＜j|H]|j＞] in Problems in Grammatical Physics > Quantum Field Theory on the Time-Axis > Quadratic Formula(not backed up) corresponds not to (d/dε) ∫Dχ Φ[χ]* Φ[χ(□ - ε)] |ε = 0 but to limε → 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 Πt.
When
Φ[χ] = Σj Πk φj(χ(k/α), k/α),
change of the phase factor of φj
φ'j(χ(k/α), k/α) = exp[iFj(k/α)]φj(χ(k/α), k/α)
changes only the whole phase factor by exp[iΣkFj(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 Time-like Direction@Products of Grammatical Physics@Grammatical Physics@Forum@Vintage(2008-2014)
The content of this article was presented by me at JPS 2013 Autumn Meeting.
 |
 |
 |
 |