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  1. B

    SE tensor for scalar field

    Oh sorry for that, I didn't mean that term is alone, it was just an example. It could be ##(\partial_\mu \phi)^2\partial_\nu \phi J^\nu## where I have an external source. My point was, what terms am I allowed to use (respecting Lorentz invariance) in the general case? I just don't know where to...
  2. B

    SE tensor for scalar field

    Homework Statement Show that if the Lagrangian only depends on scalar fields ##\phi##, the energy momentum tensor is always symmetric: ##T_{\mu\nu}=T_{\nu\mu}## Homework Equations ##T_{\mu\nu}=\frac{\partial L}{\partial(\partial_\mu\phi)}\partial_\nu\phi-g_{\mu\nu}L## The Attempt at a...
  3. B

    Stress energy tensor transformation

    Any further hint would be greatly appreciated
  4. B

    Stress energy tensor transformation

    Ok, so for the change in action we have: $$\frac{\delta S}{\delta y^\mu}=\int(\frac{\delta L}{\delta y^\mu}+\frac{\delta \partial_\alpha X^\alpha }{\delta y^\mu})$$ And the first term gives the old result. Is this ok so far?
  5. B

    Stress energy tensor transformation

    I am not sure why the change in ##\phi## is zero. When you derive E-L equations, you actually need ##\delta \phi## to be non-zero.
  6. B

    Stress energy tensor transformation

    I am a bit confused, don't I need the ##\phi##, as what I am doing is like a chain rule?
  7. B

    Stress energy tensor transformation

    Thank you for your reply. So I tried this: $$\frac{\delta(L+\partial_\mu X^\mu)}{\delta y^\nu}=\Big(\frac{\partial L}{\partial \phi}+\frac{\partial(\partial_\mu X^\mu)}{\partial \phi}-\partial_\mu\frac{\partial L}{\partial (\partial_\mu \phi)}-\partial_\mu\frac{\partial (\partial_\mu...
  8. B

    Stress energy tensor transformation

    Homework Statement Show that if you add a total derivative to the Lagrangian density ##L \to L + \partial_\mu X^\mu##, the energy momentum tensor changes as ##T^{\mu\nu} \to T^{\mu\nu}+\partial_\alpha B^{\alpha\mu\nu}## with ##B^{\alpha\mu\nu}=-B^{\mu\alpha\nu}##. Homework Equations The...
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