Abstract
This communication concerns the question of exponentials of quadratic polynomials of field operators on Fock space. This is done considering a complexification of the classical case of anti-symmetric Hamiltonians. The general quadratic polynomials are unbounded operators without properties of symmetry, and will be considered as a projective representation dΞ of some Lie algebra o2,c (H) of bounded operators S. We produce an explicit formula for the expo-nential exp (zdΞS) for z ∈ B \(\left( {0;\frac{1}{{3\left\| S \right\|}}} \right) \) and differentiating this, we find that exp (dΞ) is well defined on the Fock algebra.
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Nielsen, E.B., Rask, O. (2000). On the Existence of Exponentials of Quadratic Polynomials of Field Operators on Fock Space. In: Rebolledo, R. (eds) Stochastic Analysis and Mathematical Physics. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1372-7_8
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DOI: https://doi.org/10.1007/978-1-4612-1372-7_8
Publisher Name: Birkhäuser, Boston, MA
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