Recent content by beans73

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    What does the Lagrangian $\mathcal{L}_{eff}$ describe in particle physics?

    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...
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    Fock space and the Brillouin condition

    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'> =...
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    Nordstrom Gravity: Exploring R w/ Minkowski & Schwarzschild Metrics

    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...
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    Can a Pure Ensemble Evolve into a Mixed Ensemble?

    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 Schrodinger 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...
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    Euler angles. Quantum Mechanics Question

    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...
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    Infinite cylinder covered by one chart

    the following attachments are the working out I'm talking about...
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    Infinite cylinder covered by one chart

    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...
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    Finding eigenstates and eigenvalues of hamiltonian

    yay! thanks for your help :)
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    Finding eigenstates and eigenvalues of hamiltonian

    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...
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    Finding eigenstates and eigenvalues of hamiltonian

    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 schrodinger picture for t>0. Which my working out...
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    Can You Correctly Lower Tensor Indices Using the Metric Tensor?

    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} ??
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    Finding eigenstates and eigenvalues of hamiltonian

    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...
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