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Quantum Optics$
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John Garrison and Raymond Chiao

Print publication date: 2008

Print ISBN-13: 9780198508861

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780198508861.001.0001

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Field quantization

Field quantization

Chapter:
(p.69) 3 Field quantization
Source:
Quantum Optics
Author(s):

J. C. Garrison

R. Y. Chiao

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508861.003.0004

The cavity-mode quantization conjecture of Chapter 2 is replaced by local commutation relations — which are independent of the size and shape of the cavity — between field-operator components. This step eliminates the previous dependence on the classical boundary conditions at the ideal cavity wall. The cavity annihilation and creation operators are respectively replaced by the positive- and negative-frequency parts of the vector potential. A simple ad hoc model provides similar results for quantized fields in a passive, linear dielectric. It is shown that the total electromagnetic angular momentum cannot, in general, be expressed as the sum of well defined orbital- and spin-parts. The chapter ends with a discussion of localizability for photons, in which it is shown that there is no photon position operator, no position-space photon wave function, and no local photon number operator.

Keywords:   field-operator, local commutation relation, positive-frequency part, negative-frequency part, Heisenberg picture, angular momentum, localizability, photon position operator, photon wavefunction, local number operator

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