On a Relation among Bi-orthogonal system, Quadratic Non-Hermitian Boson operators with real spectrum and Partial PT symmetry in Fock Space

• URL: http://arxiv.org/abs/2206.01472v1
• Date: Fri, 3 Jun 2022 09:42:37 GMT
• Title: On a Relation among Bi-orthogonal system, Quadratic Non-Hermitian Boson operators with real spectrum and Partial PT symmetry in Fock Space
• Authors: Arindam Chakraborty
• Abstract summary: A new symmetry called partial PT symmetry has been considered for non-hermitian quadratic boson operators obtained from a bi-orthogonal set of vectors in C2. The symmetry behaviour has been understood in Fock space considered as a Reproducing Kernel Hilbert Space(RKHS)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A new kind of symmetry called partial PT symmetry has been considered for non-hermitian quadratic boson operators obtained from a bi-orthogonal set of vectors in C2. The symmetry behaviour has been understood in Fock space considered as a Reproducing Kernel Hilbert Space(RKHS). The reality of eigenvalues and its connection to the possibility of the aforesaid symmetry (and symmetry breaking) are studied in terms of a deformation parameter responsible for nonhermiticity

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