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For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

1 vote
1 answer
125 views

What is the name of this Lagrangian and how can I find its equations of motion?

I would appreciate if someone tell me how I should go about finding eom. for the following Lagrangian:$$L=-\frac{1}{2}\phi(\Box + m^2)\phi$$
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1 vote
4 answers
452 views

Lagrangian and finding equations of motion

I am given the following lagrangian: $L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$ and the questions asks: How many constants c can you find for which $\p …
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  • 385
2 votes

Lagrangian and finding equations of motion

Thanks to all you guys I have found that my mistake was at confusing the kinetic and interaction terms. so here is my answer to this question: this problem is basically finding the values for $\phi$ t …
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  • 385
0 votes
0 answers
42 views

expanding the coulomb lagrangian [duplicate]

suppose we have the free field lagrangian: $$L=-\frac{1}{4}F_{\mu \nu} ^2$$ then its just $$L=-\frac{1}{4}(\partial_\mu A_\nu -\partial_\nu A_\mu)^2$$ what I don't understand is how its equal to: $$L= …
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3 votes
2 answers
433 views

How to expand Maxwell Lagrangian?

I am given $$L=-\frac{1}{4}F^2_{\mu\nu}-A_{\mu\nu}J_\mu$$ to calculate equations of motion I have to expand the terms in the Lagrangian as following (note this is from Schwartz QFT book page 37): $$L= …
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