Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric
- Department of Mathematics, Hokkaido University, Sapporo 060-0810 (Japan)
We study a model of the quantized electromagnetic field interacting with an external static source {rho} in the Feynman (Lorentz) gauge and construct the quantized radiation field A{sub {mu}} ({mu}=0,1,2,3) as an operator-valued distribution acting on the Fock space F with an indefinite metric. By using the Gupta subsidiary condition {partial_derivative}{sup {mu}}A{sub {mu}}(x){sup (+)}{psi}=0, one can select the physical subspace V{sub phys}. According to the Gupta-Bleuler formalism, V{sub phys} is a non-negative subspace so that elements of V{sub phys}, called physical states, can be probabilistically interpretable. Indeed, assuming that the external source {rho} is infrared regular, i.e., {rho}/|k|{sup 3/2}(set-membership sign)L{sup 2}(R{sup 3}), we can characterize the physical subspace V{sub phys} and show that V{sub phys} is non-negative. In addition, we find that the Hamiltonian of the model is reduced to the Hamiltonian of the transverse photons with the Coulomb interaction. We, however, prove that the physical subspace is trivial, i.e., V{sub phys}=(0), if and only if the external source {rho} is infrared singular, i.e., {rho}/|k|{sup 3/2}(negated-set-membership sign)L{sup 2}(R{sup 3}). We also discuss a representation different from the above representation such that the physical subspace is not trivial under the infrared singular condition.
- OSTI ID:
- 21100256
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Local and covariant quantizations of linearized Einstein's equations. II
A C*-algebra formulation of the quantization of the electromagnetic field