Recent content by EoinBrennan

Homework Statement Given the current: J^{\epsilon}_{0} (t,x) = \overline{\psi_{L}}(t,x + \epsilon) \gamma^{0} \psi_{L}(t,x - \epsilon) = \psi_{L}^{\dagger} (x + \epsilon) \psi_{L}(x - \epsilon) with \psi_{L} = \frac{1}{2} (1 - \gamma^{5}) \psi_{D}. Use the canonical equal time...

Thank you so much, I'll be much more formal and correct about my indices.

Okay so, I have: \frac{ \lambda}{4} (\phi^{a} \phi^{a})^{2} = \frac{ \lambda}{4} (\delta_{ab}\phi^{a} \phi^{b})(\delta_{ab}\phi^{a} \phi^{b}) \frac{\partial}{\partial \phi^{a}} (\frac{ \lambda}{4} (\delta_{ab}\phi^{a} \phi^{b})(\delta_{ab}\phi^{a} \phi^{b})) \\ = \frac{ \lambda}{4}...

It's very late here, but I'll hazard a guess that they act like a symmetric term. So an anti-symmetric and symmetric terms go to 0.

So \delta\phi^{a} = \epsilon^{ab}\phi^{b} and we can get: \delta L = 0 I'm going to go through the process so that hopefully in future people will be able to find this thread to help figure out Noether currents. Process L' = \frac{1}{2}(\partial_{\mu}(\phi^{a} +...

Thank you. I thought Lambda might be a constant, does that mean the \phi in the brackets after it aren't saying a function \lambda but rather that its the constant times \phi^{4}. That actually make sense, as these questions seem to reuse Lagrangians and some of the examples I saw had this.

Okay, so after some digging and working at the problem I'm now down to a computational problem. I'm pretty sure this is the right method, but its getting me nowhere. Going through the whole problem from scratch: The Noether current J^{\mu} is: J^{\mu} = \frac{\partial L}{\partial...

An earlier part of this question asked me to get the Euler-Lagrange equations of motion. I'm unsure what \frac{\partial}{\partial \phi_{\rho}} (\lambda (\phi^{a} \phi^{a}))^{2} is though. Otherwise the equation itself seems fairly straight-forward. I get \partial_{\sigma} \partial^{\sigma}...

Homework Statement I understand the premise of Noether's theorem, and I've read over it in as many online lectures as I can find as well as in An Introduction to Quantum Field Theory; Peskin, Schroeder but I can't seem to figure out how to actually calculate it. I feel like I'm missing a...

I see. So I would get the E-L equation to be: -(∂_{\mu} ∂^{\mu} + m^{2}) ψ_{\nu} + ∂_{\mu} ∂_{\nu} ψ^{\nu} = 0 The first bit is just the Klein Gordon equation. I'm supposed to be able to show that my E-L equation implies that ∂_{\nu} ψ^{\nu} = 0. Presumably I can't just claim that...

That's great! Thanks for the help! I changed my Lagragian to be: L(\phi^{\mu}) = - \frac{1}{2} \partial_{\mu} g^{\mu \nu} g^{\mu \mu} \phi^{\mu} g^{\mu \mu} \partial_{\mu} g^{\mu \nu} \phi^{\mu} + \frac{1}{2} \partial_{\mu} \phi^{\mu} g^{\mu \nu} g^{\mu \mu} \partial_{\mu} g^{\mu \nu}...

Homework Statement Hi. I am attempting to get the Euler-Lagrange equations of motion for the following Lagrangian: L(ψ^{μ}) = -\frac{1}{2} ∂_{μ} ψ^{\nu} ∂^{μ} ψ_{\nu} + \frac{1}{2} ∂_{μ} ψ^{\mu} ∂_{\nu} ψ^{\nu} + \frac{m^{2}}{2} ψ_{\nu} ψ^{\nu} Homework Equations So, I want to get...