Graduate What is the difference between second quantization and QFT?

[fxdung]

Please teach me the difference between second quantization and QFT?

 

[atyy]

Second quantization is an equivalent language for describing non-relativistic quantum mechanics of many identical particles, which can also be described in "first quantized form" using the Schroedinger equation found in introductory textbooks. In other words, second quantization is a way of using field theoretic methods to describe the non-relativistic quantum mechanics of many identical particles.

Terminology is not very strict, and there are other usages of the term.

 

[Demystifier]

Please teach me the difference between second quantization and QFT?

The difference is more philosophical than physical. In second quantization one starts from particles as basic primitive objects and then develops mathematical tricks for efficient description of many-particle states obeying either Bose-Einstein or Fermi-Dirac statistics. These mathematical tricks can be written in terms of abstract mathematical objects called quantum fields. In QFT one starts from quantum fields as basic primitive objects and then derives that certain quantum states of those fields can be interpreted as particles obeying either Bose-Einstein or Fermi-Dirac statistics. In short,

second quantization: particles $\rightarrow$ fields
QFT: fields $\rightarrow$ particles