A Causal Alternative to Feynman's Propagator

Details A Causal Alternative to Feynman's Propagator A Causal Alternative to Feynman's Propagator

2010-12-15

arxiv.org/abs/1012.3473v1

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 3 figures

Scientific paper

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.

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