Abstract
In this section we shall analyze the general solution \(A_\mu (x)\) to Maxwell’s equations in the vacuum by choosing as gauge fixing condition the so called Coulomb gauge differently from the Lorentz gauge condition used in the general discussion of the electromagnetic field given in Chap. 5. In this new framework we shall be able to describe the electromagnetic field as a collection of infinitely many decoupled harmonic oscillators. This will pave the way for the quantization of the electromagnetic field and the consequent introduction of the notion of photon.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Recall that summation over repeated Euclidean indices \((i,\, j\,\text{ or }\,k)\), independently of their relative position, is understood.
- 2.
Notice that the \(\mathbf{P}_{\mathbf{k}}\) here have dimension \((Energy)^{\frac{1}{2}}\).
- 3.
We are anticipating the Hamiltonian formulation of the equations of motion of a mechanical system, which will be fully discussed in Chap. 8. However we assume the reader to have a basic knowledge of the Hamilton formalism which is propaedeutical to elementary quantum mechanics.
- 4.
Although we assume the reader to have a basic knowledge of non-relativistic quantum mechanics, the relevant notions will be reviewed in Chap. 9. We refer the reader to that chapter for the notations used here.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
D’Auria, R., Trigiante, M. (2016). Quantization of the Electromagnetic Field. In: From Special Relativity to Feynman Diagrams. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-22014-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-22014-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22013-0
Online ISBN: 978-3-319-22014-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)