# Quantum field theory, particle interpretations and path integrals?

I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field theory which don't use path integrals?

• Please leave the body of the question intact. You may still find helpful answers - maybe even find out that the answer you found was incorrect. It may also be helpful to people in the future. – Michael Brown Mar 14 '13 at 0:08
• John, you'll note that you edit has been rolled back. That is because we hope and expect that questions on Physics.SE will not only help the person who asked it, but also be a resource to help other in the future. Toward that end you are encouraged---if you find the answer yourself---to answer your own question so that what you have learned will be available to the next person with the same question. – dmckee --- ex-moderator kitten Mar 14 '13 at 0:09
• The particle intepretation is independent of the calculational tool. You get the same physical result using any formalism: path integral (particles are excited field configurations), canonical (particles are created by field operators acting on Fock space), Schwinger-Dyson equations (particles are poles in the Green functions), ... – Michael Brown Mar 14 '13 at 0:09
• I'm currently writing a book on the interpretation of quantum field theory (which you could read online) where you would find, in the first chapter, a formulation of quantum field theory based on the Hamiltonian formalism, so without any path integral. I think it could be interesting to you, but I don't know if you would call it a "particle interpretation"? What do you mean exactly? – Sébastien Fauvel Jun 25 '13 at 7:56

QFT is pretty much (special)relativistic quantum mechanics, so it turns out that particle number is not conserved and you can create/annihilate particles. So it's not enough to have a Hilbert space (fixed number of particles) but a Fock space (space of states of the theory) where you can have an arbitrary number of particles. $\mathcal{F} = \mathcal{H}_{1-particle} \oplus \mathcal{H}_{2-particles} \oplus \mathcal{H}_{3-particles} \oplus \ldots$