# Lagrangian of a photon?

1. Jul 11, 2015

### exmarine

I can't find this in any textbook, so I must not understand something about it. What is the Lagrangian of a photon? Would it be just h*nu?

2. Jul 11, 2015

### unknown1111

Photons have Spin 1. The general Lagrangian for Spin 1 particles is called the Proca Lagrangian and if put into the Euler Lagrange euquation yields the Proca equation. In addition, photons are massless. Therefore putting $m=0$ in the Proco yields the correct Lagrangian for photons. If you put this Lagrangian (i.e. the Proca with $m=0$ ) into the Euler Lagrange equation you get the inhomogeneous Maxwell equation.

You can find the Lagrangian, for example, here

3. Jul 11, 2015

### Orodruin

Staff Emeritus
There is no such thing as the lagrangian of a photon. Photons are quantum excitations of the electromagnetic field, which has a Lagrangian, essentially the lagrangian quoted by unknown1111.

4. Jul 11, 2015

### moss

massless spin-1 = photon, carry only a kinitic term in L ;

L=-\frac{1}{4}F^{2}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}=-\frac{1}{4}(\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})^{2}

5. Jul 17, 2015

### exmarine

OK, then how does one calculate the action (S) for the amplitude of a photon?

phi = (const) exp[(i/h_bar)S]

6. Jul 17, 2015

### Orodruin

Staff Emeritus
Which part of
was unclear? You need to specify exactly what it is you are trying to do.

7. Jul 17, 2015

### exmarine

Feynman & Hibbs, p. 29, eqn 2.15:

8. Jul 17, 2015

### exmarine

I can't seem to get the eqn editor to work.

Feynman & Hibbs, p.29, eqn 2.15: phi[x(t)] = const e^(I/h-bar)S[x(t)]

p.26: S = integral[L(x-dot,x,t) dt]

So if a photon has no Lagrangian, how does one calculate the action, amplitude, probability, etc. for a photon?

9. Jul 17, 2015

### Orodruin

Staff Emeritus
You don't. You compute the action of the electromagnetic field and correlation functions (essentially amplitudes) between different excitations of the field.

10. Jul 17, 2015

### Orodruin

Staff Emeritus
Also, you are here assuming that we have the book available and ready to open. This is not getting us anywhere.