State in electrodynamics

  • #1
I have so far encountered the notion 'state' in classical mechanics, thermodynamics and quantum mechanics. I have, however, not seen this notion in the context of electrodynamics. Is there such a thing as a state in electrodynamics? My guess is it would be a pair consisting of an electric field vector and a magnetic field vector, but I can't really substantiate this idea.
 

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  • #2
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In classical mechanics, we can associate the state of a system with a vector in phase space. If we deal with a system of point particles, we can specify the state of the system with two vectors for each particle: one for position and one for momentum. We basically compile the states of each particle into one big state vector to form the state of the overall system.

In electrodynamics, we can specify the state of the system in a similar way; just compile the states of all the individual entities appearing in the system. The main difference with an electrodynamics state is that we not only have particles but also the electromagnetic field. Since the electromagnetic field has an infinite number of degrees of freedom, this would obviously be a more complicated entity than the state of a system of particles. But if we have the state of the field (its E and B vectors at each point in space) along with the states of all the particles (their position, momentum, and charge/intrinsic magnetic moment), then we can form the state of the electromagnetic system. The space of all possible E and B configurations of the EM field constitutes the phase space for the EM field.

In many ways, describing the state of an EM field is similar to describing the state of a continuous medium or a fluid in classical mechanics.

The state in thermodynamics is a more abstract statistical definition and is not very similar to the classical and EM cases. (A single thermodynamic state would correspond to a surface, rather than a point, in phase space.) The quantum state is more similar, but it is a different kind of entity--it is a ket vector living in a Hilbert space rather than a state vector in phase space.
 
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