Creating Electrons: A Question from Feyman

[quantumfireball]

From WHERE?

"I remember that when someone had started to teach me about creation and annihilation operators, that this operator creates an electron, I said, "how do you create an electron? It disagrees with the conservation of charge"
-R.P Feymnan

I have a similar doubt someone please help

 

[Demystifier]

One should distinguish kinematics from dynamics.
Kinematically, one can conceive processes that violate any conservation law. The operator that creates a charge is such a kinematical object.
On the other hand, dynamics, including the conservation laws, is described by a Lagrangian. In a charge-conserving Lagrangian, the operator that creates an electron is allways accompanied with an operator that creates a positive charge (i.e. positron in QED), so that the total charge is conserved.

 

[quantumfireball]

Fine the hamilton operator and number operator are constants of motion.
Including the charge operator and momentum operator in the phi square non interacting field theories
For example consider a cubic cavity of volume V.
A Real scalar field ,so there are no charges
Assume there are N quanta of the scalar field within the Cavity.
Since Hamilton operator is constant of motion and hence number operator the number of quanta in the cavity are fixed at all times.
But the Question what puts the field quanta within the cavity.
ie what is the physical analogue of ak {0>
Im assuming NOn interacting langrangian
where ak is a creation operaor
Plz excuse me for being a little cryptic.

 

[meopemuk]

"I remember that when someone had started to teach me about creation and annihilation operators, that this operator creates an electron, I said, "how do you create an electron? It disagrees with the conservation of charge"
-R.P Feymnan

I have a similar doubt someone please help

The whole idea of QFT is that this theory describes systems with any number of particles within one formalism. So, in QFT there is a single Hilbert (Fock) space where all kinds of systems live together: 1-electron, 2-electron, 2 electrons +1 photon,... Particle creation and annihilation operators do not have any physical meaning (it is impossible to create particles out of nothing). They are simply convenient mathematical objects which are useful for writing compact expressions for other operators that do make physical sense: energy, momentum, number of particles, etc.

Eugene.

 

[quantumfireball]

Thanks
Doubt Cleared