This chapter discusses special features of Lorentz transformations, such as the loss of absolute simultaneity, relativistic time dilation, the clock hypothesis, and the Twin Paradox. The light cone structure of Minkowski spacetime is explored, followed by an analysis of the causal structure of solutions to the Klein-Gordon equation (the relativistic quantum wave equation that describes massive spinless particles). The chapter shows how the classical causality structure of these solutions can be encoded into a single object known as the Schwinger function, a generalized function that can be used to set up unequal time commutation relations in relativistic quantum field theory. The chapter applies Kemmer’s memory field notation to Fock’s wave-front analysis of the Klein-Gordon equation, using it to find the equation that has to be satisfied by wave front discontinuities propagating throughout spacetime.
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