What is the first and second quantization?

[Gabriel Maia]

I believe the title says it all.

What is the first and second quantization? What is the difference?

Thank you.

 

[bhobba]

First quantiization replaces position by an operator and time is a parameter. However relativity requires time and position to be treated on the same footing. Second quatiziation, aka, Quantum Field Theory, treats time and position as parameters, ie everything is a field. This way not only is relativity respected, but particles like electrons are treated in exactly the same way as EM fields that are quantisized. It was called second quantisation because originally the wavefunction was thought of as a field and was quantisized like EM fields were, but nowadays is viewed a bit differently.

Thanks
Bill

 

[atyy]

Let' say you have a system of many identical particles and you write Schroedinger's equation for them (ie. first quantization). Second quantization is simply a different way of writing the same equations, so that the symmetrization or anti-symmetrization of the wave function for identical particles is taken care of by the commutation properties of operators.

 

[bhobba]

You may also find the following of value:
http://www-physique.u-strasbg.fr/cours/l3/divers/meca_q_hervieux/Articles/Nine_form.pdf

See interpretation F: Second quantization.

Thanks
Bill