Diagonalization of the quadratic boson Hamiltonian with zero modes

J.H.P. Colpa

Physica A: Statistical Mechanics and its Applications, 1986, vol. 134, issue 2, 377-416

Abstract: The necessary mathematical equipment is developed for an analysis of the zero modes connected with hamiltonians quadratic in boson creation and annihilation operators. A “cross-matrix” being a matrix of a certain partitioned form, we consider the group G of conjuctivity transformations T, where T is a 2m-square cross-matrix subjected to the restriction T†ÎT = Î, Î : = diag(I, -I) (I is the m-square unit matrix). With respect to this group the concept of standard form is introduced for the set of positive-semidefinite hermitian cross-matrices D. It is proved that any such matrix D can be transformed into a matrix E of the standard form according to T†DT = E, T ⊆ G. An algorithm, suitable as a basis for computer programs, is given for finding standardized and standardizing matrices E and T for any given D.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:134:y:1986:i:2:p:377-416

DOI: 10.1016/0378-4371(86)90056-7

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