# Concept of field

1. Oct 5, 2005

### preet0283

can ne 1 explain 2 me the canonical formalism of generalising the concept of field in QFT...i m not 2 sure abt the replacement of generalised coordinates q(i) i=1,2,...... n with phi(x)

2. Oct 5, 2005

### masudr

I'm not sure if this view is popular, but I for one would personally appreciate if you wrote your posts in correct English as it makes it a lot easier for me to read.

I would recommend that you first gain an understanding of the classical field before you attempt to learn about a quantum system which reduces to a classical field theory in a certain limit (which is what QFT is; see 't Hooft's piece on the "conceptual basis for QFT" for further details).

Classical field theory is the generalisation of a system with finite degrees to one with infinite degrees of freedom. This is why we replace co-ordinates with a (usually) function; we have a Lagrangian density ${\cal L}$ (which is a scalar) and we try and extremize the action given by this Lagrangian so that:

$$\delta \frac{1}{c}\int{\cal L} d^4\vec{x} = 0$$

and this procedure generates field equations.

Getting to QFT is a lot more complicated, and I would recommend firstly 't Hooft's work as a brief introduction and then to dive into one of the several texts on the topic.

3. Oct 6, 2005

### preet0283

thanks for the help .........and i apologise for not writing in the correct english .... could u please tell me more about the references for QFT

4. Oct 6, 2005

### masudr

I'm sorry, but at this stage I'm only just about mastering Classical Field Theory -- EM was relatively simple (no pun intended), and GR took a bit of work. Term has started again, and I have little free time to continue my dalliances in advanced physics. QFT is my next topic of interest, but I have to learn thermodynamics, quantum mechanics and electromagnetism + optics according to the syllabus for my exams this year.

Essentially what I'm trying to say (and doing so badly) is that you'll have to ask someone else.

5. Oct 6, 2005

### robousy

f u want a gd xplanation of th canonical frmlsm then prob just check any field thry bk.

I find Mandl and Shaw and good reference.

chrs.