Hamiltonian methods in electrodynamics and quantum mechanics

P A M Dirac

Johannes A. Russer, P. Russer

Network methods are applied to establish quantum mechanical models of distributed circuits. Based on the Hamiltonian description of the Foster equivalent circuits a quantization of the equivalent circuits is performed. The quantum mechanical interaction of the modes via nonlinear elements is discussed. As an example the DC-pumped Josephson parametric amplifier is treated quantum mechanically.

Alexander Stewart

It is shown that in semiclassical electrodynamics, which describes how electrically charged particles move according to the laws of quantum mechanics under the influence of a prescribed classical electromagnetic field, only a restricted class of gauge transformations is allowed. This lack of full gauge invariance, in contrast to the situation in classical and quantum electrodynamics which are fully gauge-invariant theories, is due to the requirement that the scalar potential in the Hamiltonian of wave mechanics should represent a physical potential. Probability amplitudes and energy differences are independent of gauge within this restricted class of gauge transformation.

Jaroslav Zamastil, Jakub Benda

Alessandro Teta

B. P. Nigam

The Hamiltonian formulation of the Wheeler-Feynman theory of action at a distance in classical electrodynamics as carried out by Kerner, who has derived the nonrelativistic classical Hamiltonian for the interaction of two spinless charged particles interacting by means of half-retarded plus half-advanced potentials, has been generalized to obtain the corresponding relativistic classical Hamiltonian to order ${e}^{4}$ and ${c}^{\ensuremath{-}4}$. Using the procedure of Daughaday and Nigam, the classical Hamiltonian is transformed into the quantum-mechanical Hamiltonian operator.