Recent content by Azrael84

I don't have access to Weinberg right now, but I will check it out when I get chance. For now could you tell me then what the explicit form of the, say momentum, operator is then in the 1-particle sector, in say, position rep? Because it surely isn't just \hat{P}=-i\partial_x like in ordinary QM...

Thanks. You say "eingenvectors/eigenvalues of these operators" but what operators? the usual momentum/position operators of the fixed dimensional Hilbert space of QM, have been turned into labels. The only operators I'm aware of the field itself \phi, and I have no idea what eigenvalues...

I was already aware of the Fock space being the analogue of the Hilbert space in QFT when I originally posted. I guess what I was really wondering is what are the states in the "non-abstract sense"? e.g. in QM you could choose to work in the position rep, express the operators of your Hilbert...

Thanks.

So how do these wavefunctionals compare to the usual \mid 0\rangle, \mid k_1\rangle etc etc, type of states that one normally sees when learning QFT? are they the same thing? (is it just like in QM, where one has the wavefunction as the position representation of the abstract vector, here the...

Hello, this is quite a basic question I know, but something I'm not sure I've fully got my head around. In classical particle mechanics the dynamical variable is the position vector x, and in classical field theory the dynamical variable becomes the field \phi(x) , with x being relagated to...

OK. I see, I've never actually studied that, don't suppose you know where I can learn about it online? or any specific book references? Or if anyone could show me explicitley where to go after the point I finished at in my prev post, would be most appreciative. Thank you both for your help

Also, is it definitely Stokes I need not Gauss?

I think you have made an error here, this is the contraction of a two-tensor and one form. So no minus signs creep in on the spatial elements. As a simpler case consider conservation of particles, N^{\alpha}{}_{, \alpha}=0 which has the expanded form of \frac{\partial}{\partial t}...

Hey thanks haushofer. I can't claim to fully understand your reply, not quite at that level yet I don't think. By [dx] being an oriented surface, do you mean for example on the x term on the RHS: \int { \frac{\partial}{\partial x} T^{\alpha x } dxdydz}=\int { T^{\alpha x }...

Do you mean because I set \int {T^{\alpha \beta}{}_{,\beta} d^4x} to zero, just because the integrand was zero. When I guess it could really integrate to be a constant? This is a typo that should be T^{\alpha \beta}{}_{,\beta}= \partial_t T^{\alpha 0} + \partial_i T^{\alpha i} = 0 ...

Hey, Starting with the conversation law for the stress-energy tensor; T^{\alpha \beta}{}_{,\beta}=0 . Does anyone know how I can prove: \frac{\partial}{\partial t} \int {T^{0\alpha} d^3x} =0 for a bounded system (i.e. one for which T^{\alpha \beta}=0 outside a bounded region of...

That's an interesting way of looking at it pervect. I see it quite differently (again from the Schutz book mainly), seeing one-forms as definining constant surfaces, e.g. dx (twiddle) defines surfaces of constant x (basically the same idea as in Vector calc whereby the vector gradient defines...

Hi, How would go about arguing that the Stress-Energy tensor is actually a tensor based on how it must be linear in both it's arguments? I'm thinking it requires one 1-form to select the component of 4-momentum (e.g. \vec{E}=<\tilda{dt} ,\vec{P}> ) and also one 1-form to define the surface...

Another question I have from Schutz (CH3, 31 (c)), where he defines the Projection tensor as P_{\vec{q}}=g+\frac{\vec{q} \otimes \vec{q}}{\vec{q} \cdot \vec{q}} This can be written in component form (or rather the associated (1 1) tensor can after operating a few times on it with the metric)...