where A and B are space-like hypersurfaces that define the boundary conditions. The collection of all the φ (A) on the starting hypersurface give the initial value of the field, analogous to the starting position for a point particle, and the field values φ (B) at each point of the final hypersurface defines the final field value, which is allowed to vary, giving a different amplitude to end up at different values. This is the field-to-field transition amplitude.