Schwinger's Quantum Action Principle pp 63-90 | Cite as

# Relativistic Theory of Fields

## Abstract

This section is an adaptation of Chap. 5 of lectures given at Stanford by Schwinger in 1956 (Schwinger 1956). A state of a physical system is defined in terms of the maximum number of compatible measurements which can be made upon the system. If the state were defined on a space-like surface (one in which all points are in space-like relation: (\(\Delta x)^2-(\Delta t)^2 >0\)) then a measurement at any point is compatible with one made at any other point, since the disturbances introduced by the measurements cannot propagate faster than *c*, and hence cannot interfere. Thus, a state can be specified as an eigenvector of a complete set of commuting, Hermitian operators \(\underline{a}\), associated with a definite space-like surface \(\sigma :\,\, | a^\prime ,\sigma \rangle \). There always exists a coordinate system in which the space-like surface \(\sigma \) is all of three-dimensional space at a given time; in this particular Lorentz frame the state vector is just: \(| a^\prime ,t\rangle \).