# Mystery equation

1. Nov 29, 2009

### snoopies622

I saw this equation on one of the walls of my local physics library and I cannot make sense of it.

$$L = \bar {q} (i \gamma ^{\mu} D_{\mu} - m_{q} ) q - \frac {1}{4} F^{a}_{\mu \nu} F^{\mu \nu} _{a}$$

I tried assuming that L was the Lagrangian, m was mass, F was the Faraday tensor, etc. but my assumptions were never consistent with dimensional analysis.

What is this?

Thanks.

2. Nov 29, 2009

### nicksauce

q is a fermion field, L is the Lagrangian, gamma^u is the set of gamma matrices (http://en.wikipedia.org/wiki/Gamma_matrices), D is the gauge covariant derivative (http://en.wikipedia.org/wiki/Gauge_covariant_derivative), m is fermion mass, and F is the EM field strength tensor (or Faraday tensor) (http://en.wikipedia.org/wiki/Electromagnetic_tensor).

This is the Lagrangian for quantum electrodynamics (http://en.wikipedia.org/wiki/Quantum_electrodynamics).

For dimensional analysis: L has dimension of (mass^4), q has dimension (mass^3/2), D and m have dimension of mass, and F has dimension of (mass^2).

Last edited by a moderator: Apr 24, 2017
3. Nov 30, 2009

### snoopies622

Thanks, nicksauce. I still have so much to learn..

4. Nov 30, 2009

### nicksauce

If you continue in physics, there will be a time when this expression does not look intimidating at all.