The quadratic Fock functor
classification
🧮 math.FA
math.PR
keywords
quadraticcontractionsfockfunctorsecondsemigroupadmitanalogue
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We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
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