# Annihilation operator acting on a Fock state

1. Dec 28, 2011

### L.W.C

I'm trying to show:

a(p)|q1,q2,...,qN> =
$\sum$Ni=1(2pi)32Ep\delta(3)(p-qi)x|qi,...,qi-1,qi+1,...,qN>

I'm pretty sure you have to turn the ket into a series of creation operators acting on the vacuum |0>, but then not sure what relations need to be invoked for it to be clear.

Any help would be appreciated.

2. Dec 30, 2011

### strangerep

You might get more help if you attempt a little more yourself, according to the PF rules for homework help. For starters, write down the canonical commutation relations between the a/c operators, and the rules for how they act individually on the vacuum. Then try and do the N=2 case.

It might also help if you mention which textbook you're working from.

3. Dec 30, 2011

### L.W.C

O.K., so you just use the relation:

a(p)a+(q) = [a(p),a+(q)] + a+(q)a(p)

for each case.

Also can I just clarify that in the answer when it says:

|qi-1> if i=1, is that just ignored?

I' learning form these notes:

http://www.hep.man.ac.uk/u/pilaftsi/QFT/qft.pdf

With the aide of peskin and schroeder.

Thank you

4. Dec 30, 2011

### strangerep

OK, so now try to do the N=1 case explicitly, using equations (2.29), (2.35) and maybe (2.36) from P&S.

I think it's the vacuum $|0\rangle$.