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Please explain to a stupid dummy a very simple thing.

Take an a photon in 1+3 dimensions. How DOF it has? We all know that 2. How we calculate it?

a) 1) We have a spin 1 particle that should have 2s+1=3 spin state. So DOF=3.

2) We have 4 A_{μ}guys. One is out because of gauge invariance. So we have 3 left.

Does EOM gives us smth?

3) Electromagnetic tensor has 4×4 components. Its anti-symmetric so 4*3/2=6 components left. Bianci identities F_{(αβ;γ)}=0 gives us C_{4}^{3}=4!/3!1!= 4 conditions (is it true? Or it is 6eq? Its the same as a symmetry conditions???), so we left with 2 DOF.

4) Electric and magnetic fields have three components each so we have 6. (4 Maxwell equations? ->2 )

What about photon in 1+D dim? Where and how zero photon mass get into play?

b) For graviton in 1+3.

1) h_{αβ}has 16 components. The matrix is symmetric so 4*5/2=10 components left. Bianci gives us h_{[αβ;γ]}=0 - 4 equations. The gauge conditions (i.e. coordinate transformations with non zero Jacobian) gives me 4 tranformation (1 for each coordinate). Left with 2 - Fine

2. In the 1+4 the same calculation give

5*6/2=15 (symetric matrix)

15-5=10 (because of gauge)

Bianci gives us how?

How DOF in the 5dim case????

Help!!!

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# Electron and graviton degrees of freedom

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