The Classical Electromagnetic Field Hamiltonian
نویسنده
چکیده
In these notes we motivate the necessity for quantizing the electromagnetic field, we outline a procedure for doing that, and then we carry out the classical part of that procedure, which is to find a classical Hamiltonian for the combined system of matter plus electromagnetic field. In a subsequent set of notes we shall quantize this classical Hamiltonian and study the results. Standard references for the material in these notes include Heitler, The Quantum Theory of Radiation and Cohen-Tannoudji, Dupont-Roc and Grynberg, Photons and Atoms.
منابع مشابه
Electromagnetic Field Quantization & Applications to the Casimir Effect
The quantization of the electromagnetic field is demonstrated through a two-pronged approach. The classical harmonic oscillator is discussed in depth, and then its quantization is further discussed. Additionally, the classical electromagnetic field Hamiltonian is derived and analogized to the classical harmonic oscillator Hamiltonian at several points. Quantization of the electromagnetic field ...
متن کاملLagrangian and Hamiltonian Formulation of the Classical Electromagnetic Field
In Notes 38, we derived the classical Hamiltonian description of the classical electromagnetic field by starting with the equations of motion and making a series of guesses for the Hamiltonian and the canonical variables. A more systematic, but more lengthy, procedure is to start with the classical Lagrangian for the field and proceed through the Legendre transformation. This procedure is outli...
متن کاملFinite dimensional Hamiltonian formalism for gauge and field theories
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the pataplectic Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized Poisson p-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of p-brackets. As illustration of our ...
متن کاملIs there a preferred canonical quantum gauge?
The interaction between a long solenoid and a charged particle in the field free region outside it is studied treating both systems quantum mechanically. This leads to a paradox which suggests that when the electromagnetic field is quantized, there may be a preferred quantum gauge for the vector potential. This paradox is resolved by canonically quantizing the system in a different gauge in whi...
متن کاملClassical relativistic systems of charged particles in the front form of dynamics and the Liouville equation
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description is reduced by use of the geometrical concept of the forms of rel-ativistic dynamics. The remainder gauge degrees of freedom of the electromagnetic potential...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016