Particle interpretation of quantized field

Florian A. Scheck

Hrvoje Nikolić

The relativistic effects of the integer-spin quantum field theory imply that the wave functions describing a fixed number of particles do not admit the usual probabilistic interpretation. Among several most popular interpretations of quantum mechanics applied to first quantization, the only interpretation for which this fact does not lead to a serious problem, and therefore the only consistent interpretation of first quantization, is the de Broglie-Bohm interpretation.

Gilles Labonté

We review the main recent results concerning the capacity of the quantized field system in the presence of an external field to represent physical particles at all times. We deal more particularly with the Dirac spin 1/2 equation since it is known to be trouble free at the c number level. As this had not been done explicitly before, we present a proof, valid for a wide class of potentials, which shows that at each time a Fock basis for individual energy quanta (the physical particles) exists in the same Hilbert space, i.e. the system can be completely described in terms of these.

Shûkô Azuma

Richard Healey

This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The difficulty stems from the problems of interpreting any quantum field theory. Even the non-relativistic quantum mechanics of particles is a theory whose interpretation remains at best controversial, and at worst simply lacking. Interpretations of quantum field theory face the additional hurdle that it is not clear what the theory is about: neither a field nor a particle ontology is readily squared with the mathematics of the theory. The chapter explores the status of loop representations in several approaches toward the interpretation of quantum field theory.

Sergei Vladimirovich Tyablikov