Hi,
I don't know much about the standard model but I'm asking out of interest. Why do we actually need a Lagrangian for the standard model? Surely when you apply the relevant Euler-Lagrange equations, you end up with a variety of equations like the Maxwell equations or Dirac equations. Why...
So the first term of the Lagrangian is proportional to ##{F_{\mu \nu}}{F^{\mu \nu}}##. I wrote out the matrices for ##{F_{\mu \nu}}## and ##{F^{\mu \nu}}## and multiplied at the terms together and added them up, but some of the terms didn't cancel like they should have. Should I have used minus...
The problem:
$$\mathcal{L} = F^{\mu \nu} F_{\mu \nu} + m^2 /2 \ A_{\mu} A^{\mu} $$
with: $$ F_{\mu \nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu} $$
1. Show that this lagrangian density is not gauge invariance
2.Derive the equations of motion, why is the Lorentzcondition still...
I'm trying to derive the Klein Gordon equation from the Lagrangian:
$$ \mathcal{L} = \frac{1}{2}(\partial_{\mu} \phi)^2 - \frac{1}{2}m^2 \phi^2$$
$$\partial_{\mu}\Bigg(\frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi)}\Bigg) = \partial_{t}\Bigg(\frac{\partial \mathcal{L}}{\partial...
How does one write a Lagrangian of a coherent state of vector fields (of differing energy levels) in terms of the the individual Lagrangians?
I desperately need to know how to know to do this, for a theory of mine to make any progress.
Please stick with me, if I didn't make sense just ask...
In quantum field theory (QFT) from what I've read locality is the condition that the Lagrangian density ##\mathscr{L}## is a functional of a field (or fields) and a finite number of its (their) spatial and temporal derivatives evaluated at a single spacetime point ##x^{\mu}=(t,\mathbf{x})##...
I have been reading these notes: http://isites.harvard.edu/fs/docs/icb.topic455971.files/l10.pdf
in which they claim that if two spacetime events are coincident in one frame of reference then they are coincident in all inertial frames of reference, thus spacetime events are absolute i.e. they...
I am slightly unsure as to whether I have understood the notion of locality correctly. As far as I understand it locality is the statement that if two events occur simultaneously (i.e. at the same time) then no information can be shared between them (they are causally disconnected). Thus a...
Homework Statement
I have to expand the following term:
$$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$
to get in the end this form...
I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...