  The Feynman propagator used in the conventional in-out formalism in quantum
field theory is not a causal propagator as wave packets are propagated
virtually instantaneously outside the causal region of the initial state. We
formulate a causal in-out formalism in quantum field theory by making use of
the Wheeler propagator, the time ordered commutator propagator, which is
manifestly causal. Only free scalar field theories and their first quantization
are considered. We identify the real Klein Gordon field itself as the wave
function of a neutral spinless relativistic particle. Furthermore, we derive a
probability density for our relativistic wave packet using the inner product
between states that live on a suitably defined Hilbert space of real quantum
fields. We show that the time evolution of our probability density is governed
by the Wheeler propagator, such that it behaves causally too.
