Classical Mechanics and Field Theory

2018 ◽  
pp. 603-690
Author(s):  
Mattias Blennow
Keyword(s):  
Field Theory ◽  
Classical Mechanics

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

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.

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.

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.

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