Re: On the wave function of the photon
- From: "Zigoteau" <zigoteau@xxxxxxxxx>
- Date: Tue, 31 May 2005 06:38:01 +0000 (UTC)
Hi, Ben,
You've received a number of erudite answers to your questions, but I
thought I could add something fresh to the question of Fock space.
> 1a. How is Fock space actually related to QFT, if at all?
Fock space is one representation of the space of all possible state
vectors. Very often, there is a refusal to talk about particular
representations of state vector space, because this is felt to be a bit
pedestrian. However I still feel the need for a particular basis so as
to get a gut feeling for what's going on, and I think I'm not alone.
Basically, you just need to know the representation of creation and
annihilation operators on a given element G of Fock space, which has
N-particle component G_N(X1, X2, . . . , XN) . Each operator has an
'orbital' which I will symbolize B(X). For the annihilation operator b
, you just integrate out the last argument:
bG_N-1 =3D Integral_all space{G_N(X1, X2, . . . , XN)*b(XN)*dXN}
For the creation operator b^+, you form all products permuting the
extra argument, and (anti)symmetrize appropriately:
b^+G_N+1 =3D Sigma_r=3D0^N {(=B11)^r*G_N(X1, X2, . .Xr-1,Xr=3D1, . . ,
XN+1)*B(Xr)}
b and b^+ do the things they're supposed to to each other, and if you
have other orthonormal orbitals, with them too.
> It's described in
> textbooks as a way to make a relativistic quantum theory that allows fo=
r the
> creation and annihilation of particles, but all the successful relativi=
stic
> quantum theories are field theories, which don't have particles in the =
first
> place.
Well, the emphasis is on the math, but at the end of the day they have
as many and as few particles as the Schr=F6dinger multiparticle
equation. If you define a field as something which has a value at each
point in space, then the Schr=F6dinger equation is a field theory.
Cheers,
Zigoteau.
.
- Follow-Ups:
- Re: On the wave function of the photon
- From: Zigoteau
- Re: On the wave function of the photon
- References:
- On the wave function of the photon
- From: Ben Rudiak-Gould
- On the wave function of the photon
- Prev by Date: Re: Wave Function of the Universe?
- Next by Date: Re: length of wavetrain of single photon
- Previous by thread: Re: On the wave function of the photon
- Next by thread: Re: On the wave function of the photon
- Index(es):
Relevant Pages
|
|
