Quantum Field Theory

Quantum field theory emerges in a very natural and straightforward way from our general probabilistic setting. We have already seen that very simple unique jump chains or probabilistic cellular automata, like the transport automata, describe twodimensional quantum field theories for free massless fermions. Actually, it is the quantum field theory which arises directly at the most basic level. Single-particle quantum mechanics is obtained as a special case or approximation, rather than being the starting point, as in the historical development of quantum field theory. The generic situation for interesting probabilistic systems describes states with many particles, with a continuum limit admitting an infinite number.