The action principle in quantum theory

[Dyson]

Hello!

I wonder is there exist a way to deduct the conserved current equation, generator of

the symmetry transformation and so on from a total quantum L with the help of action

principle?

Many books i have seen deduct the physical quantity from the classical L or construct

the quantum generator from the comparasion with classical one.


Thanks for reply!

 

[tom.stoer]

What you call "quantum L" is called effective action in the path integral formalism. There are so-called Ward-identities corresponding to a "quantized charge conservation". But the construction of the conserved charge is always done before quantization = at the classical level.

Within quantum (field) theory one has to proof that the corresponding operator identities / Ward-identities continue to exist w/o anomaly.

The path integral formalism is rather close to the classical one when it comes to conserved quantities as it is based on an action integral, no operators.

 

[Dyson]

What you call "quantum L" is called effective action in the path integral formalism. There are so-called Ward-identities corresponding to a "quantized charge conservation". But the construction of the conserved charge is always done before quantization = at the classical level.

Within quantum (field) theory one has to proof that the corresponding operator identities / Ward-identities continue to exist w/o anomaly.

The path integral formalism is rather close to the classical one when it comes to conserved quantities as it is based on an action integral, no operators.

Thanks! You give me a guide to learn more knowledge on effective action!