First, second and third quantization formalisms

[dpa]

Hi all,

I was curious about mathematics and physical meaning behind first and second quantization formalisms of Schrödinger's equation. what do these mean?

Okey, third quantization formalism may be weird/new for many but its associated with wheeler dewitt equation.

 

[cgk]

First&second quantization: There are different details associated with these names, depending on the field you are looking for.

When working with a finite or countably infinite Hilbert space as one-particle basis (on which the Fock spaces are expanded) and having a fixed number of particles[1], then first- and second quantization are entirely equivalent. The latter is then a reformulation of the former which intrinsically takes care of fermionic or bosonic symmetries (and by doing that makes dealing with determinants or permanents much easier). This is the form of second quantization you will encounter in many body physics of the condensed matter and chemical varieties, and there is really no mystery at all. However, my understanding is that in QFT, people tend to interpret more into second quantization, but I have never entirely understood how this differs from the straight-forward "normal" second quantization.

Of a third quantization I have never heard.

[1] Additonally, in second quantization you can have pure wave functions with a non-determinate number of particles, but in first quantization you cannot. How relevant this is depends on the application.

 

[lugita15]

See here for an advanced explanation.

 

[dpa]

See here for an advanced explanation.

Well that was pretty easy to grab.

Uhh. well.. except for ... the ... you know that part with... everything!