# Electric field of a photon. Why does polarization make sense?

So for a long time, I thought the photon had an electric field. I thought this because there are calculations done in quantum optics where you define terms like $\langle 0 | \mathbf{E}|1\rangle$ to be the measurement of a single photon in a detector. I always viewed this as an electric field measurement since the electric field operator is in in the braket.

However I just learned that the photon does not have an electric field, but is rather a carrier of the electromagnetic field (or an excitation of the electromagnetic field). So if a photon doesn't have an electric field, how can a photon have a polarization? The polarization vectors in the quantum mechanical version of the electric field are mathematically the same as the classical polarization vectors. So if the photon has no electric field, how does the concept of polarization make any sense???

• I would dispute the statement "the photon does not have an electric field". Can you say where you "learned" this? Preferably with a specific quote and reference. – Steve Byrnes Nov 9 '16 at 16:31
• It deals with my research. One of my committee members said "The photon does not have an electric field, and neither a magnetic field… because it is a neutral particle… The electromagnetic fields are made of photons, but that is different. " – user41178 Nov 9 '16 at 16:34
• The field is polarized. The photon is an excitation of the field. I understand what your committee member said, but I find that to be a disagreeable point of view. It might be correct in some sense, but it is too glib. – garyp Nov 9 '16 at 16:42
• You are mixing incommensurable viewpoints: An electric and magnetic field with definite values only exists in the classical description, in which there is no photon. In the quantum field theoretic setting where there are photons, there are no definite electric and magnetic fields. It's not clear what the meaning of "The photon has/doesn't have an electric field" is actually supposed to be. – ACuriousMind Nov 9 '16 at 17:31
• The QM view and their description of what a photon is is one of the possible descriptions. In the "classical view a photon has both a magnetic and an electric field. – HolgerFiedler Nov 10 '16 at 6:11