Puzzled about electromagnetic field behaving like oscillators

[commutator]

i am having some problem in unerstanding a concept explained in my book in the chapter harmonic oscillators. as an example of this, it says, is the electromagnetic field, where A (vector potential) plays the role of the co ordinate and its dot plays the role of velocity in the oscillator hamiltonian.i found this pretty strange , because i do not understand how we get such a hamiltonian? i mean, only when we write hamiltonian of a particle , we get terms containing its momentum and position co -ordinates.but how are we writing the hamiltonian of an electromagnetic field?how do we get A and A dot here?where is the particle here?i am pretty confused. someone please help me out.many thanks in advance.

 

[matonski]

This is classical field theory. I found a really good introduction by Leonard Susskind here. They are also available on iTunes U. The course is called Special Relativity, but he really only goes over SR in the first lecture. The rest is classical field theory. Electromagnetism is covered in lectures 7 and 8.