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【SEOテキスト】宇田雄一,06.2.12,§1-3.時間発展と描像,[4]IN描像とOUT描像,(0)前提条件,t>T1ort<T2⇒H1(t)=0(T1>T2),�@基底と表示,(�@)B(in)(t)≡{|e(in)(f;t)>|f∈I},B(out)(t)≡{|e(out)(f;t)>|f∈I},|e(in)(f;t)>≡U0(t,T2)|e(H)(f;T2)>=U0(t,T2)U(T2)|e(s)(f)>,|e(out)(f;t)>≡U0(t,T1)|e(H)(f;T1)>=U0(t,T1)U(T1)|e(s)(f)>,(�A)|Ψ>≡∫dnfψ(in)(f;t)|e(in)(f;t)>≡∫dnfψ(out)(f;t)|e(out)(f;t)>,Ω|e(in)(f;t)>≡∫dngω(in)(g;f;t)|e(in)(g;t)>,Ω|e(out)(f;t)>≡∫dngω(out)(g;f;t)|e(out)(g;t)>,�Aベクトルと演算子,|Ψin(t)>≡∫dnfψ(in)(f;t)|e(s)(f)>=[U0(t,T2)U(T2)]-1|Ψ>,|Ψout(t)>≡∫dnfψ(out)(f;t)|e(s)(f)>=[U0(t,T1)U(T1)]-1|Ψ>,Ωin(t)|e(s)(f)>≡∫dngω(in)(g;f;t)|e(s)(g)>,∴Ωin(t)=[U0(t,T2)U(T2)]-1ΩU0(t,T2)U(T2),Ωout(t)|e(s)(f)>≡∫dngω(out)(g;f;t)|e(s)(g)>,∴Ωout(t)=[U0(t,T1)U(T1)]-1ΩU0(t,T1)U(T1),�B時間発展,(�@)|Ψin(t)>≡|Ψs(t)in(t)>,Ωin(t)≡Ω(t)in(t),|Ψout(t)>≡|Ψs(t)out(t)>,Ωout(t)≡Ω(t)out(t),|Ψin(t)>=|ΨH>(t≦T2),|Ψout(t)>=|ΨH>(t≧T1),Ωin(t)=ΩH(t)(t≦T2),Ωout(t)=ΩH(t)(t≧T1)