- #1

- 188

- 1

**Quantization of Gauge theories ??**

Hi , i am trying to learn the math formalism of Gauge Theories

as far as i know they begin with the 1-form

[tex] A= \sum_{i} T^{i}A_{\mu}^{i} [/tex]

where 'T_i ' are the generators of the Lie Group

then we define the 2-form [tex] F= dA + (1/2)[A,A] [/tex]

and the equation of motion are [tex] dF =0 [/tex] (exterior derivative of F ) and [tex] *d *F = J [/tex]

with J being an external source and [tex] *F_{ij}=e_{ijkl}F^{kl} [/tex] Hodge Star operator

QUESTION:

=========

How can you define a Hamiltonian of Your Gauge theory if the Lagrangian is equal to [tex] tr[F^{ab}F_{ab}] [/tex]

how can you apply the Quantization to these theories ??