On the equivalence of different hamiltonians for the semi-classical radiation theory

This paper is based on the idea that wave mechanics is primarily suitable for giving an indirect description of nature. The world to which the equations of the, theory here proposed are directly applicable is an unnatural one, containing sources and sinks of matter which give to its radiational laws a symmetry lacking in nature. The theory may be regarded as consisting of two postulates. The first (which may, if desired, be regarded as a definition) specifies the character and properties of an unnatural assembly of systems, each consisting of an electron in a static potential field U . It states that, of the energy radiated in an elementary solid angle of standard magnitude, the part which will pass through an analyzer which transmits the component of electric field in a given direction (perpendicular to the line of observation) is determined by applying the usual Schrödinger interpretations (of density, current and material energy) to a Schrödinger equation perturbed by a term which is a certain constant multiplied by the electric field, in that direction, acting on the electron, due to the potential field U . (For comparison with classical radiation theory, it will be noted that the perturbation term vanishes in any region in which, from the classical standpoint, the electron is not accelerated, in that direction, by the field U ). In the process of specifying the radiation from the assembly, the Schrödinger interpretations will have specified also the nature and magnitude of the sources and sinks of electrons (each in a field U ). Their presence is due, mathematically speaking, to the multiplying constant mentioned above being a complex quantity. From these results the properties of a natural assembly are specified by means of the second postulate, which states that when the sources and sinks are removed, any process which in their absence is meaningless or physically inconceivable will cease, and all other processes will remain unaffected. The calculation is readily extended to include the effect of an external field of radiation. The theory requires no representation of radiation other than the Maxwellian wave, and will be free from the difficulties encountered in other theories.

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The Classical Radiation Theory of B(3)

The Enigmatic Photon ◽

10.1007/978-94-010-9840-3_5 ◽

1996 ◽

pp. 89-117

Author(s):

Myron W. Evans ◽

Jean-Pierre Vigier ◽

Sisir Roy ◽

Stanley Jeffers

Keyword(s):

Radiation Theory ◽

Classical Radiation

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Bound state quantum electrodynamics with polarization sources

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1975.0015 ◽

1975 ◽

Vol 342 (1628) ◽

pp. 113-129 ◽

Cited By ~ 9

Keyword(s):

Electromagnetic Fields ◽

Quantum Electrodynamics ◽

Relativistic Quantum ◽

Bound State ◽

Magnetic Interactions ◽

Conventional Theory ◽

Relativistic Quantum Field Theory ◽

Atomic Systems ◽

Radiation Theory ◽

Classical Radiation

A manifestly gauge invariant relativistic quantum field theory of the interaction of atomic systems with electromagnetic fields is shown to be systematically obtained from conventional quantum electrodynamics. The basic ingredient is an exact decomposition of the Dirac sources J μ modified to include the binding, into polarization sources P and M . The transformation of the conventional theory is achieved by means of a generalized Power-Zienau-Woolley transformation. While J μ couple to the potentials A μ , the polarization sources are shown to couple directly to the field intensities E and B . An explicit separation between electric and magnetic interactions is thus obtained which is in close correspondence w'ith the case in the semi-classical radiation theory. The relevance of the transformed theory to problems involving intense electromagnetic fields is pointed out and discussed.

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The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

Scientific Reports ◽

10.1038/s41598-021-83916-4 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Souma Jinno ◽

Shuji Kitora ◽

Hiroshi Toki ◽

Masayuki Abe

Keyword(s):

Numerical Method ◽

Time Domain ◽

Maxwell Equations ◽

Three Dimensional ◽

New Formalism ◽

Vector Potentials ◽

Lumped Parameter ◽

Radiation Theory ◽

Stable Solutions ◽

The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

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