Recent content by beans73

I've been given the following lagrangian: \mathcal{L}_{eff} = \bar{\psi}(i\gamma^{\mu}\partial_{\mu} - m)\psi - \frac{G}{4}(\bar{\psi}\psi)(\bar{\psi}\psi) where I have been told that the coefficient G is real and has mass dimension -2. I will eventually need to derive the feynman rules...

Hi there! in a recent lecture on fock space, i was given the brillouin condition for two-particle operators:- <\Phi_{0}|a^{†}_{a}a_{r}h|\Phi_{0}> = \frac{1}{2}\sum\sum<\Phi_{0}|a^{†}_{a}a_{r}a^{†}_{\lambda}a^{†}_{\mu}a_{\lambda'}a_{\mu'}|\Phi_{0}><\lambda\mu|g|\mu'\lambda'> =...

Homework Statement Question: "A theory of gravity devised by physicist G. Nordstrom, relates g_{μ\nu} to T^{μ\nu} by the equation: R=κg_{μ\nu}T^{μ\nu} where the metric has the form g_{μ\nu}=e^{2\Phi} with \Phi=\Phi(x^{μ}) a function of the spacetime coordinates (the special form of the...

Homework Statement Hi there. just working on a problem from sakurai's modern quantum mechanics. it is: A) Prove that the time evolution of the density operator ρ (in the Schrödinger picture) is given by ρ(t)=U(t,t_{0})ρ(t_{0})U^\dagger(t,t_{0}) B) Suppose that we have a pure ensemble at...

hi there. i have been working on this problem recently, but i seem to have a slightly different answer to the one above. my working out led me to have a minus sign in the relation between G and J: after taking the taylor expansion of the exponentials and relating the \epsilon^{2} coefficients...

the following attachments are the working out I'm talking about...

Hi there. I have just been doing some reading on manifolds, and I'm finding some of it hard to grasp. An example we were given was of the infinite cylinder and how to construct its map, and that it would be with one chart. the reading initially says that we can use θ \in (0,2pi] and z \in...

yay! thanks for your help :)

oh ok then. would this be the right plan of action then? using the eigenvectors i found for the hamiltonian|E_{1}> = (1,1) and |E_{2}> = (1,-1). i then constructed: ||E_{1}> = |a'> + |a''> and |E_{2}> = |a'> - |a''> ( i have left out the normalization constant here) then i can...

thanks for that. i have actually continued on with this problem, and I've come across another question. i found the eigenvalues to be ±∂. the problem then asks b) suppose the system is known to be in state |a'> at t=0. write down the Schrödinger picture for t>0. Which my working out...

Homework Statement I have a tensor X^{μ\nu} and I want to make this into X_{μ\nu}. Can I do this by simply saying X_{μ\nu}=\eta_{μ\nu}\eta_{μ\nu} X^{μ\nu} ??

Hey there, the question I'm working on is written below:- Let |a'> and |a''> be eigenstates of a Hermitian operator A with eigenvalues a' and a'' respectively. (a'≠a'') The Hamiltonian operator is given by: H = |a'>∂<a''| + |a''>∂<a'| where ∂ is just a real number. Write down the eigenstates...