Dear Sourabh,

   The electromagnetic field Fba (a,b=0,1,2,3) is the same in quantum fields too. At quantum level the electromagnetic field is treated as an ordinary classical electromagnetic field coming from the potentials, only its Fourier components are quantized (photons) as colletion of harmonic oscillators, leading to creation and annihilation operators for photons (Fock space). Thus you can see how the electrons and the photons interact using perturbative methods (Feynman diagrams) or so on, but what that you are going to have new is a quantum interpretation of the fields at very small scales.

   I hope that this can help

"Tensor" is just a representation of the physical laws and it is preferred by physicists since the obvious question is why would mother nature favor a particular coordinate system over another? Tensor formulation just makes coordinate transformations easier, eg. from cartesian to polar coordinates. All fundamental physical laws must be invariant under coordinate transformations, and so must yield the same result.

Most quantum phenomenon are affected by EM field, so obviously if you study quantum field theory (QFT) and quantum electrodynamics (QED), you will encounter EM field "tensor" quite often!

Tensor is a mathematical model that is used much in postmodern physics. The problem is if that model is adequate to represent the physical reality. It would seem tensor would have to guarantee the invariance of laws of physics under any transformation of coordinates, but here there is confusion between the principle of invariance and the principle of covariance. Physical phenomena happen in nature in one only way but the description of those phenomena by different observers isn't alwyas the same because of the presence of causes that change phenomenon passing from a reference frame to another. Only the Principle of Relativity and nothing other guarantees the invariance of laws of physics with respect to reference frames and observers who are inertial, i.e. provided with uniform relative motion each other. If one then wants to apply tensor to QM it is a question of choices.

Thank you a lot Vikash Pandey and Dr. Daniele. 

Yes it  is invariant. But if electric field & magnetic fields are made up of virtual photons, so do we have tensor EM tensor by considering QM? Or classical electric and magnetic fields gives accurate results? And we can happily work with E-M tensor while applying it to QM.

@ Sourbabh

You did not read the answers carefully. Tensor is just a form of "representation". And for the other query, let me ask you a counter question, what is the mathematical difference between a EM field related to "virtual" photons (as you call it!) and classical EM fields?

   Dear Sourabh,

   The electromagnetic field Fba (a,b=0,1,2,3) is the same in quantum fields too. At quantum level the electromagnetic field is treated as an ordinary classical electromagnetic field coming from the potentials, only its Fourier components are quantized (photons) as colletion of harmonic oscillators, leading to creation and annihilation operators for photons (Fock space). Thus you can see how the electrons and the photons interact using perturbative methods (Feynman diagrams) or so on, but what that you are going to have new is a quantum interpretation of the fields at very small scales.

   I hope that this can help

@Dr. Danial, Thanks a lot sir. I got it.

@ Vikash: What we observe is classical wave which have many photons. But while considering QED, photon have probability amplitude which rotates and according to phase, it gives maxima or minima. I was confused by this because i thought may be some more exact formulation for electric field is there (if we consider virtual photon). Btw, I am in 1st year, msc so limited knowledge. But solving something related to this. Just want to confirm if presence of virtual photon gives different results for electric fields. Thanks a lot.

   Dear Sourabh,

   Don't be worry with the virtual photons, they are just some mathematical tools which don't follow the usual dispersion low

          c=λν

in fact they cannot be called particles at all. Their real interest is because they can be exchanged carrying momentum by electric charges, in such a form that explains the electromagnetic interaction between them. Only Heisenberg's indeterminacy law ought to be followed when using them.

@Daniel,

Thanks a lot sir. Sir, if you are interested the question which is given below, then can you tell me about this?

Does E=pc is followed by particles only or waves also follow this relation?

https://www.researchgate.net/post/Does_Epc_is_followed_by_particles_only_or_waves_also_follow_this_relation

Dear Sourbah, 

Yes, the electromagnetic tensor is used quite a lot in quantum field theory (and its generalizations for the weak and strong forces). At the classical level it obeys the same maxwell's equations as a classical field, but once the theory is quantized it has to be treated differently. Unlike some of the other respondents, I would like to stress that the tensorial nature of the electromagnetic field is rather important (or at least convenient) when one writes a theory (i.e. an action) that contains the electromagnetic force. Because you want your action to be Lorentz invariant, you can only use certain combinations of the electromagnetic tensor (or the four-potential) which are scalars. I guess one could do this explicitly using E and B fields but it will become very difficult very fast (especially since you have to maintain gauge-invariance as well).

Sometimes, when the electromagnetic field is very very strong, you can even use the classical field without quantizing it and assume it is a classical field, and then perform your other computations quantum-mechanically, but this is of course an approximation.

Hope this helps!

Omri

     Dear Sourbah,

     If you take the formula E=pc, you assume that the rest mass of the particle is zero, which happens e.g. for the photon. Notice that the photon is a particle. But the photons can also be considered waves, this means that this formula is true for both: waves and particles. What is important is to consider that in both cases the rest mass has to be zero.

     Sorry for the delay, I didn't realized that I had this question.

thanks u @Dr. Daniel & Omri.