Quantum fluctuations of a Coulomb potential
Abstract
Quantum fluctuations of the electromagnetic field produced by an elementary particle are investigated. Using the Schwinger-Keldysh formalism, it is found that the two-point correlation function of the Coulomb potential has a nonvanishing value already at zeroth order in the Planck constant. It is proved that to this order, the correlation function is gauge independent and has a well-defined coincidence limit. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly. Furthermore, the spectrum of the electromagnetic fluctuations is investigated. It is found, in particular, that in a wide range of practically important frequencies, the spectral density of the electromagnetic field fluctuations exhibits an inverse frequency dependence. It is shown also that in the case of a macroscopic body, the ℏ0 part of the correlation function is suppressed by a factor 1/N, where N is the number of particles in the body. Relation of the obtained results to the problem of measurability of the electromagnetic field is mentioned.
- Publication:
-
Physical Review D
- Pub Date:
- June 2005
- DOI:
- 10.1103/PhysRevD.71.113012
- arXiv:
- arXiv:hep-th/0402178
- Bibcode:
- 2005PhRvD..71k3012K
- Keywords:
-
- 12.20.-m;
- 42.50.Lc;
- Quantum electrodynamics;
- Quantum fluctuations quantum noise and quantum jumps;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 15 pages, 2 figures