19.—Classical Electromagnetism—How should One Teach It Today?

1972 ◽  
Vol 70 ◽  
pp. 207-217
Author(s):  
N. Kemmer
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Magnetic Property ◽  
Classical Theory ◽  
Classical Mechanics ◽  
Teaching Experience ◽  
Classical Electromagnetism ◽  
Physics Students ◽  
Vector Calculus ◽  
Mathematical Techniques

SynopsisThe author maintains that a course in the classical theory of the electromagnetic field, with full exploitation of vector calculus methods, should be thought of as being as much of a basic essential in any physics honours course as is a course on classical mechanics. It is suggested that if the mathematical techniques are taught in a way that relates them directly to the central notions of field theory and avoids discussion of special techniques, the mathematical burden is sufficiently light to be borne by all physics students, not only those theoretically inclined. The course need not be of excessive length if it is understood as exclusively an introduction to field concepts and hence not to cover in any detail the electric and magnetic property of materials. A number of particular ideas arising from the author's teaching experience are discussed.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

Field theory, classical

2018 ◽  
Author(s):  
Mark Wilson
Keyword(s):  
Field Theory ◽  
Twentieth Century ◽  
Electromagnetic Field ◽  
Physical Quantity ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Classical Mechanics ◽  
Electrical Strength ◽  
Mass Temperature

A physical quantity (such as mass, temperature or electrical strength) appears as a field if it is distributed continuously and variably throughout a region. In distinction to a ’lumped’ quantity, whose condition at any time can be specified by a finite list of numbers, a complete description of a field requires infinitely many bits of data (it is said to ’possess infinite degrees of freedom’). A field is classical if it fits consistently within the general framework of classical mechanics. By the start of the twentieth century, orthodox mechanics had evolved to a state of ontological dualism, incorporating a worldview where massive matter appears as ’lumped’ points which communicate electrical and magnetic influences to one another through a continuous intervening medium called the electromagnetic field. The problem of consistently describing how matter and fields function together has yet to be fully resolved.

A new classical theory of electrons

1951 ◽  
Vol 209 (1098) ◽  
pp. 291-296 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Classical Theory ◽  
Physical Significance ◽  
Gauge Transformations

In the theory of the electromagnetic field without charges, the potentials are not fixed by the field, but are subject to gauge transformations. The theory thus involves more dynamical variables than are physically needed. It is possible by destroying the gauge transformations to make the superfluous variables acquire a physical significance and describe electric charges. One gets in this way a simplified classical theory of electrons, which appears to be more suitable than the usual one as a basis for a passage to the quantum theory.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

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