Concept of Field: Canonical Formalism in QFT

[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)

 

[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.

 

[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

 

[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.

 

[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.