Relativistic Theory of Fields

  • Kimball A. MiltonEmail author
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


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: \(| a^\prime ,t\rangle \).

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Homer L. Dodge Department of Physics and AstronomyThe University of OklahomaNormanUSA

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