TL;DR
This paper introduces a purely algebraic kernel calculus for the bosonic Fock representation of complex Hilbert spaces, enabling derivation of integral kernel formulas for metaplectic operators in the complex-wave setting.
Contribution
It develops an algebraic kernel calculus for bosonic Fock spaces and applies it to derive known integral kernel formulas for metaplectic operators.
Findings
Established a purely algebraic kernel calculus for bosonic Fock spaces
Reproduced standard integral kernel formulas for metaplectic operators
Demonstrated the calculus within the complex-wave representation
Abstract
We show that the bosonic Fock representation of a complex Hilbert space admits a purely algebraic kernel calculus; as an illustration, we use it to reproduce the standard integral kernel formulae for metaplectic operators within the complex-wave representation.
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Taxonomy
TopicsQuantum optics and atomic interactions · Spectral Theory in Mathematical Physics · Cold Atom Physics and Bose-Einstein Condensates