- #1
mhill
- 189
- 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 ??
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 ??