摘要
在作者一篇论文中,曾经指出,含有高阶微商的薛定谔方程的建立是有困难的,但这并不意味着不能在作用表示的波动方程中直接引入高阶微商.在这篇短文中,我们考虑电子场与电磁场的作用而在作用表示的波动方程中直接引入无穷高级微商.这样的理论的目的并不在乎获得任何可以与实验比较的结果.事实上。
The purpose of this short note is to see whether,starting from a wave equation i=/(t)ψ=-∫d^3x[A_μf(□)ieN(γ_μψ)]ψ (notation in the above equation and in the following same as those in book on quantum electrodynamics) which is different from the customary one in quantum electrodyna- mics by an extra factor f(□)(□ being ~2/x_μx_μ,f(□)being an arbitrary function of □),one may proceed to calculate the different terms in the S matrix,the self-energy,etc.in the usual fashion.Of course the only interesting case is that in which f(□)is not a polynominal,so that f(□)ieN(γ_μψ) at the point x depends on ieN(γ_μψ) at other space-time points. In course of calculation,it is found necessary to introduce a symbol T_(xx′)A(x″)B(x′″) defined as δ_μA(″B(x′″) if X_0>X′_0 δ_pB(x′″)A(x″) if X_0<x′_0 where x,x′refer to other two space-time points (other than x″,x′″),and similar T sequences for a product of 3 or more operators.It is shown that such a T sequence may be developed in a series of N sequences and that one may proceed to calculate the various terms in the S matrix,nearly in the same manner as when f(□) is absent.Whereas self energies may be rendered finite by appropriate choice of f,the vacuum polarization remains infinite.
出处
《北京师范大学学报（自然科学版）》
CAS
1957年第2期53-60,共8页
Journal of Beijing Normal University(Natural Science)
