By Volodimir Simulik

A suite of essays within which invited participants try and outline the character of the electron, the quantum particle that has defied characterization for almost a century.

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Orthonormality and equivalence are used 1 Ecore = = Ecore = ∫ N N ∫ 1 N N ∫ ∑ϖ d ′ ⎧ N ⎩ c =1 ∫ Ψ ⎪⎨⎪ ∑ω d ψ † ( xd ′ d ′ ′ c ⎧ ) ⎪⎨ ⎪ ⎩ ⎫ c ⎪ core Hˆ (c )ϖ ⎬⎪ Ψdx c ⎭ N ∑ω c ⎫ c ⎪ core Hˆ (c )ϖ ⎬ ⎪ ⎭ c =1 ∑ω ψ d ( xd ) dxc ⎡ a ρ (x ∫ ⎢∑ ε (x ) ρ (x ) ⎢⎣ i ψ 1 ( x1 ) Hˆ core (1)ψ 1 ( x1 ) dx1 = † d d i i = ε core ( x1 ) ρ1 ( x1 ) dx1 (formal definition) 2 i 1 core 1 1 1 1 )⎤ ⎥ ρ ( x ) dx ⎥⎦ 1 1 1 24 Jaime Keller For the electron-electron interaction (e-e), because the equivalence of the N electrons and using the expansion of the ψ, we obtain N ∑ϕ 2 Eint = e2 (1)α i∗ ∑ ϕ ∗j (2)α ∗j ∗ i i x12 j ∑ϕ (2)α k ∑ ϕl (1)α l dx1 dx 2 .

T Hooft, in Recent Developments in Gauge Theories, edited by G’t Hooft (Plenum, New York, 1980, p. 135; H. Terazawa, Prog. Theor. Phys. 64, 1763 (1980). [5] H. Terazawa, in Ref. [4]. [6] W. D. Peccei and T. Yanagida, Phys. Lett. B124 , 67, (1983); R. Barbieri, A. Masierro and G. Veneziano, ibid. O. N. Mohapatra and M. Yasue, ibid. B128, 65 (1983). [7] H. Terazawa, J. Phys. Soc. Jpn. 55, 4249 (1986); H. Terazawa and M. Yasue, Phys. Lett. B206, 669 (1988); H. Terazawa in Perspectives on Particle Physics, edited by S.

A11, 2463 (1996). [18] H. Terazawa, in Ref. [1]. [19] H. Terazawa, Mod. Phys. Lett. A7, 3373 (1992). [20] Y. , Phys. Rev. Lett. 81, 1562 (1998). For a review see, T. Kajita and Y. Totsuka, Rev. Mod. Phys. 73, 85 (2001). [21] B. Pontecorvo, Zh. Eksp. i Teor. Fiz. 33, 549 (1957) [Soviet Phys. JETP 6, 429 (1958)]; 34, 247 (1958) [7, 172 (1958)]; 53, 1717 (1967) [62, 984 (1968)]; Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28, 870 (1962). H. Ahn et al. (K2K Collaboration), Phys. Lett. H.

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