【SEOテキスト】宇田雄一「古典物理学」e1の定義:e1=e1(N1×F1×F4,n×R({1,・・・,n})×R(2))∀(t,i)∈N1;∀f∈F2,1;∀m∈R(2×1);∀n∈N;∀Z∈F4,n;∀M∈R({1,・・・,n});e1(t,i;f(□,□,1),Z,M,m(□,1))=e2(t,i,1;f,Z(N3),m)+m(1,1)n∑j=1M(j)γ(i;f(t,□,1),Z(t,□,j)),e2の定義2:∀n∈N;∀f∈F2,n;∀E∈F3;∀m∈R(2×{1,・・・,n});∀(t,i,k)∈N2,n;∀p∈Pn;∀g∈F4,n-1;∀M∈R({1,・・・,n-1});【1】⇒【2】【1】(n≧2)and
p(n)=k and g(N3)=E and∀j∈{1,・・・,n-1};[g(N1,j)=f(N1,p(j))and M(j)=m(1,p(j))]【2】e2(t,i,k;f,E,m)=e1(t,i;f(□,□,k),g,M,m(□,k)),e3の定義1:∀ξ∈N01;∀f∈F3;∀n∈N;∀Y∈F2,n;∀q∈R({1,・・・,n});(q=0)⇒[【1】and【2】]【1】∀i∈3;e3(ξ,i,1;f,Y,q)=3∑j=13∑k=1ε(i,j,k)∂jf(ξ,k,1)+∂4f(ξ,i,2)and
e3(ξ,i,2;f,Y,q)=3∑j=13∑k=1ε(i,j,k)∂jf(ξ,k,2)-∂4f(ξ,i,1)【2】∀i∈2;e3(ξ,i,3;f,Y,q)=3∑j=1∂jf(ξ,j,i),e3の定義2:∀ξ∈N01;∀f∈F3;∀n∈N;∀Y∈F2,n;∀q∈R({1,・・・,n});【1】and【2】and【3】and【4】【1】∀i∈3;e3(ξ,i,1;f,Y,q)=e3(ξ,i,1;f,Y,0)【2】∀i∈3;e3(ξ,i,2;f,Y,q)=e3(ξ,i,2;f,Y,0)-n∑j=1q(j)∂4Y(ξ({4}),i,j)δ(ξ(3)-Y(ξ({4}),□,j))
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