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Posted

The link does not work.

 

So I don't know what you have done, but it is extremely useful to write the Lagrangian (density) as differential form on the total space of a jet bundle. This differential form is known as the Poincare-Cartan n-form.

 

You can then form all the Euler-Lagrange equations in terms of geometry, in fact in terms of the Lie derivative of the Poincare-Cartan form.

 

What does Lagrangian mean in terms of modern and theoretical physics?

 

The Lagrangian is a function of the fields and their derivatives and is assumed to contain all the physical information about the system both classically and quantum mechanically. The hard part is extracting this information!

Posted
What does Lagrangian mean in terms of modern and theoretical physics?

 

To expand on ajb's answer, as an example, the Lagrangian for QED is:

 

[math] {\cal L} = -\frac{1}{4}F^{\mu \nu} F_{\mu \nu} + \bar \psi \left( i \gamma^\mu \partial_\mu +m \right) \psi [/math]

 

In principle, everything you need for QED is in that formula (once you define the notation) - it completely specifies the theory (which is quite neat I think).

 

Edit: the link works fine for me.

Posted
To expand on ajb's answer, as an example, the Lagrangian for QED is:

 

[math] {\cal L} = -\frac{1}{4}F^{\mu \nu} F_{\mu \nu} + \bar \psi \left( i \gamma^\mu \partial_\mu +m \right) \psi [/math]

 

In principle, everything you need for QED is in that formula (once you define the notation) - it completely specifies the theory (which is quite neat I think).

 

Edit: the link works fine for me.

 

QWT, too:eyebrow:

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