Register to reply

Scalar QCD

by abrata
Tags: scalar
Share this thread:
Apr22-14, 02:31 PM
P: 1
Hi all,

I am currently trying to calculate the beta function for scalar QCD theory (one loop for general su(n)).

I therefore need to calculate the Feynman rules in order to apply them to the one loop diagrams. Unfortunately I am getting very confused with what the Lagrangian for scalar QCD should be. If anyone knows of some clear examples of this Lagrangian and possibly the derivation of the corresponding Feynman rules and diagrams I would be very appreciated.

Many thanks
Phys.Org News Partner Physics news on
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Bubbling down: Discovery suggests surprising uses for common bubbles
New non-metallic metamaterial enables team to 'compress' and contain light
Apr22-14, 03:07 PM
P: 855
First start with the Lagrangian for a scalar field with an internal SU(N) symmetry:

[tex](\partial_\mu \phi^a)^\dagger (\partial^\mu \phi^a) - m^2 \phi^{a \dagger} \phi^a - \frac{\lambda}{4}(\phi^{a\dagger} \phi^a)^2[/tex]

Then replace the partial derivatives with covariant derivatives:

[tex](D_\mu \phi^a)^\dagger (D^\mu \phi^a) - m^2 \phi^{a \dagger} \phi^a - \frac{\lambda}{4}(\phi^{a\dagger} \phi^a)^2[/tex]

where ##D_\mu \phi^a = \partial_\mu \phi^a - i g T^{a b} \phi^b##. Add in the gauge field Lagrangian and you have the Lagrangian for scalar QCD.

Srednicki's textbook has some chapters on scalar electrodynamics, which might help you.

Register to reply

Related Discussions
Riemann curvature scalar, Ricci Scalar.What does they measure ? Special & General Relativity 4
Finding the geodesic function for scalar * function= scalar Advanced Physics Homework 0
Lagrangian, scalar or pseudo-scalar? Quantum Physics 1
Decay rate of a scalar particle under scalar/pseudoscalar lagrangian Advanced Physics Homework 0
From the scalar of curvature (Newman-Penrose formalism) to the Ricci scalar Special & General Relativity 8