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The content of this page was developed in Uda Equation of Dirac Field @ Quantum History Theory @ Problems. The Hamiltonian: H = ∫d^{3}x ψ†(x)γ^{0}(i The quantization conditions: [ψ_{α}(x), ψ†_{β}(y)]_{+} = δ_{αβ}δ^{3}(x  y), [ψ_{α}(x), ψ_{β}(y)]_{+} = 0. The above expressions are of the existing theory. Now I start explaining my theory of quantum history. [ψ_{α}(x), ψ†_{β}(y)]_{+} = δ_{αβ}δ^{4}(x  y), [ψ_{α}(x), ψ_{β}(y)]_{+} = 0. I assume so by seeing [Z(t), Z†(t')]_{+} = δ(t  t') and [Z(t), Z(t')]_{+} = 0 in Uda Equation of Fermionic Mechanics. The left hand side of Uda equation: i = i = i = i I assume so by seeing i The concept is to shift all spacetime points at which there is a particle by ε in timelike direction. Because (γ^{0}γ^{0})_{αβ} = δ_{αβ}, the left hand side of Uda equation is ∫d^{4}x ψ†(x)γ^{0}(i Uda Equation: ∫d^{4}x ψ†(x)γ^{0}(i ∴ ∫d^{4}x ψ†(x)γ^{0}(i ∴ ∫d^{4}x ψ†(x)γ^{0}(i ∴ ∫d^{4}x ψ†(x)γ^{0}(i This expression was first published in 15th @ May 2019 @ News at about 2019/05/15/15:00(Japan Standard Time). In case, below I note down details. [ψ_{α}(x), ψ†_{β}(y)]_{+} = ψ_{α}(x)[ψ_{β}(y)]† + [ψ_{β}(y)]†ψ_{α}(x) = δ_{αβ}δ(x^{1}  y^{1})δ(x^{2}  y^{2})δ(x^{3}  y^{3})δ(x^{0}  y^{0}). [ψ_{α}(x), ψ_{β}(y)]_{+} = ψ_{α}(x)ψ_{β}(y) + ψ_{β}(y)ψ_{α}(x) = 0. ∫_{∞}^{∞}dx^{1}∫_{∞}^{∞}dx^{2}∫_{∞}^{∞}dx^{3}∫_{∞}^{∞}dx^{0} Σ_{α=1}^{4}Σ_{β=1}^{4} [ψ_{α}(x)]† [i σ_{1}σ_{2} = σ_{2}σ_{1} = iσ_{3}, σ_{2}σ_{3} = σ_{3}σ_{2} = iσ_{1}, σ_{3}σ_{1} = σ_{1}σ_{3} = iσ_{2}, σ_{1}σ_{1} = σ_{2}σ_{2} = σ_{3}σ_{3} = σ_{0}. ( [γ^{μ}, γ^{ν}]_{+} )_{αβ} = (γ^{μ}γ^{ν} + γ^{ν}γ^{μ})_{αβ} = 2g^{μν}δ_{αβ}, g^{00} = 1, g^{11} = g^{22} = g^{33} = 1, μ≠ν ⇒ g^{μν} = 0. 

Author Yuichi Uda, Write start at 2019/05/18/15:19JST, Last edit at 2019/05/20/16:46JST  






