2000/02/29 by Marek Czachor
Physics and Astronomy · #Canonical quantization #Hamiltonian (control theory) #Harmonic oscillator #Noncommutative and Quantum Gravity Theories #QED vacuum #Quantization (signal processing) #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics #Quantum field theory #Renormalization #Vacuum state #cond-mat #hep-th #physics.atom-ph #quant-ph
paper · pdf · doi:10.1088/0305-4470/33/45/307
published as J.Phys.A33:8081-8104,2000 · Completely rewritten version of quant-ph/0002003v2. There are overlaps between the papers, but sections on perturbative calculations show the same problem from different sides, therefore quant-ph/0002003v2 is not replaced
arxiv created 2000/03/20 · openalex publication_date 2000/11/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 built-in 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.