Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 20

As we now show, the wave equation (3.1) presents a number of problems which will eventually lead us to abandon it.

Locality

The wave equation (3.1) has an unwanted property: In order to determine the change in the solution at the point in an infinitesimal time interval (t, t + dt), we must know the function for time t at all points . This property is contained in the Taylor expansion of the Hamilton operator in powers of the Laplacian and is referred to as non-locality. It is also evident from the form of the solution (3.4) by noting that

which upon using the Taylor expansion in p² becomes