The Lagrangian is an important tool used throughout quantum field theory. You can get a leg up in your studies by learning or reviewing the basics of Lagrangian dynamics. This is covered in chapter 2 of Quantum Field Theory Demystified, which is available for download here.

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## 3 comments:

after going over the chapter i wondered how one finds the lagrangian in the first place. instead one is given the langrangian.

In the book you're given the Lagrangian for the purpose of starting there to do other tasks. In general, you can write down the Lagrangian from the kinetic and potential energies.

Dear David,

Your QFT-D has helped me a lot in getting a closer understanding of spinors.

However, one thing that’s not clear from the many books I’ve read that discuss spinors (nor from questions to the AdvancedPhysicsForum and the Usenet/Google Group science.physics.research), is:

How can spinors exist for massive objects, when their explanation seems to rest on Cartan’s initial writings in which he bases the parameterisation of spinors on isotropic vectors (effectively the same parameterisation as yours at the very bottom of page 65 of QFT-D).

Similarly in GR presentations, such as MTW’s chapter on spinors in their aptly massive book

"Gravitation", (and usually given as a rehash of Penrose’s Flagpole+Flag+OER model, from Penrose and Rindler, Vol1) the idea that the flagpole is on the lightcone (and therefore an isotropic vector) can only apply to massless spinors (photons or maybe gluons) as nothing with mass can occupy the lightcone.

So how can one discuss spinors with mass (=fermions only, now?), if they can’t correspond to an isotropic vector in spacetime?

Or are they “isotropic vectors” only in some other parameter space (spin space? particle-antiparticle space…?)

Yours sincerely – Paul G. Ellis

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