Transition between Quantum Mechanics and QFT

[Silviu]

Hello! I just started reading a book about QFT by Peskin (it was recommended by one of my physics professor and I saw that MIT course on QFT also uses it). However they start right away with Klein-Gordon equation suggesting that I should be familiar with it. I took 2 classes on quantum mechanics (in which I finished the Griffith book) and I was mentioned about Klein-Gordon equation a bit (just that it is a relativistic form of Schrödinger equation and some basic stuff) but I didn't do anything deep about it. I was wondering what should I read to be able to make the transition from Quantum Mechanics to QFT? Thank you!

 

[vanhees71]

Where do you have trouble with Peskin and Schroeder? It should be ok, if you have attended QM1. You can ask questions in the quantum forum here at PF.

 

[Silviu]

Where do you have trouble with Peskin and Schroeder? It should be ok, if you have attended QM1. You can ask questions in the quantum forum here at PF.

It is not that I have problems in understanding. They explain stuff pretty clear, the thing is that many times they put it like: "You should be familiar with this, but we will still describe it briefly here". For example the lagrangian associated with KG equation is not hard to understand, but they suggest that I should have already known it, from my QM class, which I don't. I was just wondering if there is any intermediate step that I missed. Thank you!

 

[vanhees71]

Don't worry about such "pedagogical" talk. As long as you understand it, it's fine. As I said, one great thing of this forum is that you can ask questions, and maybe somebody can help.

 

[dextercioby]

@Silviu there's no link between QM and QFT nowadays, for the fail of specially relativistic Quantum Mechanics is not a subject of too many books. It might seem that the Klein-Gordon Lagrangian density is pulled out of the hat, but if you already know the field equations, then there's little room for the Lagrangian density. The standard requirements: real function of fields, cannot contain 3 derivatives (the field equations have only 2), must be local (the field and its derivatives must be evaluated at the same spacetime point).

The book by Peskin and Schroeder is a standard in teaching, but I think a shorter book could also serve good and clear explanations. Lewis Ryder wrote a good book, and also Pierre Ramond.

 

[vanhees71]

If the question is, why the Lagrangians look as they look, then one has to study the representation theory of the Poincare group. Wigner's original paper is already very readable:

E. P. Wigner, On Unitary Representations of the Inhomgeneous Lorentz Group, Annals of Mathematics, 40 (1939), p. 149.
http://dx.doi.org/10.1016/0920-5632(89)90402-7

Then there's a very good treatment in Weinberg, Quantum Theory of Fields, vol. 1.