C SMALL CHARGED SPHERE: Lorentz Force Delta tau, retarded time interval DEBUG VERSION File: dtau Input: none, this is first Output: tau1.o, tau2.o, tau3.o, in the file tau.z Starting date: November 7, 1987 Last revision: November 11, 1987 The retarded proper time interval (a negative quantity) is computed as a function of the proper position, using the light-cone interval R dot R. The proper position is alpha = eps*n, where n is a unit 3-vector. A dtau=5,eps=5 ! dtau=5,eps=5 to keep leading nonsingular term A c,tau1,tau2,tau3 I mu,nu,la V y,u,a,j,R,n F D1y,D2y,D3y,D1u,D2u,D1a A norm B eps Common RdotR,tau1.o,tau2.o,tau3.o *fix C P lists Z RdotR = R(mu)*R(nu) Id, R(mu~) = - D1y(mu,n)*eps - D2y(mu,n,n)*eps^2/2 - D3y(mu,n,n,n)*eps^3/6 - u(mu)*dtau - D1u(mu,n)*eps*dtau - D2u(mu,n,n)*eps^2*dtau/2 - a(mu)*dtau^2/2 - D1a(mu,n)*eps*dtau^2/2 - j(mu)*dtau^3/6 Id, Addfa, D(mu,nu) Id, uDu = c^2 Id, uDa = 0 Id, uDj = -aDa Id, D1u(u,l~) = 0 Id, D1a(u,l~) = -D1u(a,l) Id, D2u(u,l~,m~) = -D1u(la,l)*D1u(la,m) Id, dtau = tau1*eps + tau2*eps^2 + tau3*eps^3 Id, D1y(mu~,n~)*D1y(mu~,n~) = - norm*norm + D1y(u,n)*D1y(u,n)/c^2 Id, tau1 = - norm/c - D1y(u,n)/c^2 ! Solution for tau1 verified by ! killing the coefficient of ! eps^2. Sum mu,la *next Z RdotR = RdotR Z tau1.o = - norm/c - D1y(u,n)/c^2 Id, Commu, D1y,D2y,D3y,D1u,D2u,D1a B tau2 *next Z tau2.o = RdotR*norm^-1*eps^-3*c^-1/2 + tau2 Id, eps = 0 B eps *next Z RdotR = RdotR Id, tau2 = tau2.o C *next C Z RdotR = RdotR Id, Commu, D1y,D2y,D3y,D1u,D2u,D1a *end