Quantisation of the Electromagnetic Field and Spontaneous Photon Emission

2021 ◽  
pp. 4-23
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Electromagnetic Field ◽  
Excited State ◽  
Physical Interpretation ◽  
Gauge Invariance ◽  
Photon Emission ◽  
Perturbation Expansion ◽  
Atomic State ◽  
Abstract Concepts ◽  
Free Electromagnetic Field ◽  
Physical Result

We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

scholarly journals Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems

2020 ◽  
Vol 27 (4) ◽  
pp. 902-911
Author(s):  
V. G. Bagrov ◽  
D. M. Gitman ◽  
A. A. Shishmarev ◽  
A. J. D. Farias
Keyword(s):  
Electromagnetic Field ◽  
Synchrotron Radiation ◽  
Dirac Equation ◽  
Photon Emission ◽  
Quantum States ◽  
Photon Radiation ◽  
Electric Currents ◽  
Scalar Particles ◽  
Two Photon ◽  
The Relationship

Synchrotron radiation was originally studied by classical methods using the Liénard–Wiechert potentials of electric currents. Subsequently, quantum corrections to the classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, an intermediate approach is considered, in which electric currents generating the radiation are considered classically while the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases; it allows one to study one-photon and multi-photon radiation without complicating calculations using corresponding solutions of the Dirac equation. Here, exact quantum states of an electromagnetic field interacting with classical currents are constructed and their properties studied. With their help, the probability of photon emission by classical currents is calculated and relatively simple formulas for one-photon and multi-photon radiation are obtained. Using the specific circular electric current, the corresponding synchrotron radiation is calculated. The relationship between the obtained results and those known before are discussed, for example with the Schott formula, with Schwinger calculations, with one-photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating two-photon synchrotron radiation.

Sign in / Sign up

Export Citation Format

Share Document