Recent content by div curl F= 0

I'm having a problem calculating the Feynman amplitude for the scalar scattering process \chi^+ \chi^- \to \chi^+ \chi^- for an interaction Lagrangian which is: \mathcal{L} = - g \chi^\dagger \chi \Phi - \frac{\lambda}{4} (\chi^\dagger \chi)^2 So far I have the 2 Feynman Diagrams for...

Is there an identity for a product of 2 LC Tensors in 4D if one sums over 3 of the indicies? i.e. \epsilon^{\mu \beta \gamma \delta} \epsilon_{\nu \beta \gamma \delta} = ? What if gamma is constrained to be 0? Does this reduce things? Best Regards

If the action of a theory is invariant under a transformation (i.e. a lorentz transformation or a spacetime translation), does this imply that the Lagrangian is also invariant under the transformation? L \to L + \delta L \;\;;\;\; \delta L = 0?

Dear RedX and haushofer, I have infact done the calculation in this way; separating out the zero cases and i,j not equal to zero cases but this has a big knock on effect on the next part of the calculation, making a very large equation out of a very small number of terms. I just thought there...

Dear All I'd be very grateful if someone could help me out with finding the trace of a product of 4 SL(2,C) matrices, namely: \mathrm{Tr} \left[ \sigma^{\alpha} \sigma^{\beta} \sigma^{\gamma} \sigma^{\delta} \right] where: \sigma^{\alpha} = (\sigma^0, \sigma^1, \sigma^2, \sigma^3)...

I'm having a memory blank on this particular area of field theory. Is the product of two spinors a scalar or scalar type entity and if so, can I treat it like a scalar? (i.e. move it around without worrying about order etc) i.e. is \Phi_1^{\dagger} \Phi_1 a scalar? and if so does...

I worked the time derivative out to be: \displaystyle \frac{\partial \phi}{\partial t} = - i \sum_n \sqrt{\frac{E_n}{2L}} \left[ a_n e^{-i(E_n t - k_n z)} - a_n^{\dagger} e^{+i(E_n t - k_n z)} \right] Whilst integrating the whole expression I set t = 0 to remove the time dependence (as...

Dear all, I'd be very grateful for some help on this question: "The momentum operator is defined by: \displaystyle P = - \int_{0}^{L} dz \left(\frac{\partial \phi}{\partial t}\right) \left( \frac{\partial \phi}{\partial z} \right) Show that P can be written in terms of the operators a_n...

Thanks for your reply lbrits. That transformation: D_{\mu} \to g D_{\mu} g^{-1} looks suspiciously like an equivalence relation from group theory?

Dear All, I'd be grateful for a bit of help with the following problems: Consider the Lagrangian: \displaystyle \mathcal{L} = (\partial_{\mu} \phi) (\partial^{\mu} \phi^{\dagger}) - m^2 \phi^{\dagger} \phi where \phi = \phi(x^{\mu}) Now making a U(1) gauge transformation...

I'd be greatful for a bit of help on this question, can't seem to get the answer to pop out: A particle moving in a potential V is described by the Klein-Gordon equation: \left[-(E-V)^2 -\nabla^2 + m^2 \right] \psi = 0 Consider the limit where the potential is weak and the energy is...

Thank you for your reply. My metric does indeed vary with the coordinates.

Does it make sense for the Ricci Scalar to be a function of the spacetime coordinates? In previous calculations I have carried out in the past, everytime the Ricci Scalar has been returned as a constant, rather than being explicitly dependent on the coordinates. Thanks for any replies

Not too sure if this is solvable in general as you only have 2 equations but 3 unknowns. Are there any other equations/constraints that you didn't post up? Generally, you need n equations/constraints to solve for n unknowns.

Homework Statement "Write down the operator \hat{a}^2 in the basis of the energy states |n> . Determine the eigenvalues and eigenvectors of the operator \hat{a}^2 working in the same basis. You may use the relation: \sum_{k = 0}^{\infty} \frac{|x|^{2k}}{(2k)!} = cosh(|x|) "...