Abstract
In this paper, we give an expression for canonical transformation group with Grassmann variables, basing on the Jacobi hsp ≔ semidirect sum hN⋊sp(2N,R)C algebra of boson operators. We assume a mean-field Hamiltonian (MFH) linear in the Jacobi generators. We diagonalize the boson MFH. We show a new aspect of eigenvalues of the MFH. An excitation energy arisen from additional self-consistent field parameters has never been seen in the traditional boson mean-field theory. We derive this excitation energy. We extend the Killing potential in the Sp(2N,R)CU(N) coset space to the one in the Sp(2N+2,R)CU(N+1) coset space and make clear the geometrical structure of Kähler manifold, a non-compact symmetric space Sp(2N+2,R)CU(N+1). The Jacobi hsp transformation group is embedded into an Sp(2N+2,R)C group and an Sp(2N+2,R)CU(N+1) coset variable is introduced. Under such mathematical manipulations, extended bosonization of Sp(2N+2,R)C Lie operators, vacuum function and differential forms for extended boson are presented by using integral representation of boson state on the Sp(2N+2,R)CU(N+1) coset variables.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.