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A toy model of bosonic non-canonical quantum field

Marek Czachor·Monika Syty
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Abstract

A harmonic oscillator is an indefinite-frequency one if the parameter $ω$ is replaced by an operator. An ensemble of $N$ such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies associated with a given problem are present already in a single oscillator and $N$ can be finite. Due to the operator character of $ω$ the resulting algebra of creation-annihilation operators is non-canonical. In the limit of large $N$ one recovers perturbation theory formulas of the canonical quantum field theory but with form factors automatically built in. Vacuum energy of the ensemble is finite, a fact discussed in the context of the cosmological constant problem. Space of states is given by a vector bundle with Fock-type fibers. Interactions of the field with 2-level systems, including Rabi oscillations and spontaneous emission, are discussed in detail.

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Marek Czachor, Monika Syty. 2001-12-02. A toy model of bosonic non-canonical quantum field. https://arxiv.org/abs/hep-th/0112011

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