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...
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...
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|) "...