Second Quantization for Non-relativistic Identical Particles

Ph. Droz-Vincent

R. MacKenzie, Prasanta Kumar Panigrahi, Manu B. Paranjape +1 more

А. Г. Нураматов, Прохоров Лев Васильевич

It is shown that quantization of the dynamical systems with second class constraints can be reduced to quantization of systems with first class constraints. The motion of a non-relativistic particle along the plane curve and on a surface is considered. The results axe identical to those of the «thin layer» method. Influence of the non-physical variables on the physical sector is discussed.

Fabio Benatti, Roberto Floreanini B, Ugo Marzolino

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.

Victor Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest systems with a large number of particles.