Unequal time em field commutators in quantum optics

J. D. Cresser*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The unequal time commutators of the field operators of the free electromagnetic field, and their physical interpretation in terms of the simultaneous measurability of the EM field components at different space time points, have long been known since the work of Jordan and Pauli, and Bohr and Rosenfeld. The behaviour of these commutators can be understood in terms of the field of uncertain strength unavoidably generated as a consequence of a measurement of field strength in some region in space time. This field propagates freely in space, and if present in some other region in space time at which another field measurement is made, will affect the outcome of this measurement in an uncontrollable way.In the presence of matter, these unequal time commutators are modified, with readily understandable consequences for the measurability properties of the field. When calculating these commutators, the matter can be treated in two different ways. First of all is the case in which the matter occurs in bulk as in a macroscopic dielectric, with the quantized description of the EM field obtained by imposing classical boundary conditions on the EM field. The second case is that in which the matter is treated quantum mechanically. In both cases, the modified commutators contain terms whose physical significance can be understood as representing the effect of the field generated by a field measurement being scattered by the matter present. Thus one measurement can affect another either through the disturbing field propagating freely from one space time region to the other, or through the scattering of this field.In this paper, an outline is given of the general kinds of results obtained, how they can be obtained in each case, and where the results have played a role in determining the behaviour of certain quantum systems including the Glauber model of a photodetector, and in the theory of frequency filtered photon detection.

Original languageEnglish
Pages (from-to)52-57
Number of pages6
JournalPhysica Scripta
Issue numberT21
Publication statusPublished - 1 Jan 1988


Dive into the research topics of 'Unequal time em field commutators in quantum optics'. Together they form a unique fingerprint.

Cite this