square173205 Posted November 17, 2007 Share Posted November 17, 2007 Although the expressions of Lagrangian for quarks and leptons in the standard-model are very sophisticated, the mixture of indices for Lorentz space and inner space sometimes makes difficult to develop equations. To get better perspective, I tried to rewrite the Lagrangian with the differential form in the following site; http://hecoaustralia.fortunecity.com/lagrangian/gauge4.htm Link to comment Share on other sites More sharing options...
Severian Posted November 17, 2007 Share Posted November 17, 2007 I suppose it depends on what you are used to. I find the traditional form much more intuitive. Link to comment Share on other sites More sharing options...
ydoaPs Posted November 17, 2007 Share Posted November 17, 2007 What does Lagrangian mean in terms of modern and theoretical physics? Link to comment Share on other sites More sharing options...
ajb Posted November 17, 2007 Share Posted November 17, 2007 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! Link to comment Share on other sites More sharing options...
Severian Posted November 17, 2007 Share Posted November 17, 2007 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. Link to comment Share on other sites More sharing options...
ydoaPs Posted November 17, 2007 Share Posted November 17, 2007 Edit: the link works fine for me. Sometimes it works, sometimes it doesn't. Link to comment Share on other sites More sharing options...
square173205 Posted November 18, 2007 Author Share Posted November 18, 2007 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: Link to comment Share on other sites More sharing options...
timo Posted November 18, 2007 Share Posted November 18, 2007 QED = Quantum Electrodynamics, in case that was your question. Link to comment Share on other sites More sharing options...
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