Non-canonical quantum optics

Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of the electromagnetic field by means of such a non-CCR algebra automatically removes the infinite energy the of vacuum but still results in a theory which is very similar to quantum electrodynamics. An analysis of perturbation theory shows that the non-canonical theory has an automatically builtin cut-off but requires charge/mass renormalization already at the non-relativistic level. A simple rule allowing one to compare perturbative predictions of canonical and non-canonical theories is given. The notion of a unique vacuum state is replaced by a set of different vacua. Multi-photon states are defined in the standard way but depend on the choice of vacuum. Making a simplified choice of the vacuum state we estimate corrections to atomic lifetimes, probabilities of multiphoton spontaneous and stimulated emission and Planck's law. The results are very similar to the standard ones but there are also differences which can be tested experimentally. Two different candidates for a free-field Hamiltonian are compared.