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The IMA volumes in mathematics and its applications

Lie Algebraic Approach to the Many-Electron Correlation Problem

Josef Paldus

Published Jan 1, 1988• 45 citations
Publisher
DOI
10.1007/978-1-4684-6363-7_10

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A new formulation of the many-electron correlation problem is presented based on the use of parastatistics. It is shown that second-order para-Fermi creation and annihilation operators, which correspond to the creation and annihilation of spin-averaged paraparticles, occur naturally for the spin-independent many-electron problem. Moreover, the spin-independent many-electron Hamiltonian is directly expressible in terms of the parafield operators. The structure of the general para-Fermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n+1, 1). Finally, an explicit matrix representation for the para-Fermi algebra of order 2, which enables one to handle even particle-number-nonconserving operators, is obtained in a canonical U(n)-adapted basis.
Electronic Correlation in Molecules - Some Fundamental Problems Improving the Panoply of Quantum Chemical Methods for the Study of Correlated Extended Systems Lie-Algebraic Structure and the Coupled Cluster Method Configuration Interaction Studies Using Biorthogonal Approach to VB Basis Optimised Virtual Orbitals for the Calculation of Molecular Properties of Excited Electronic States A Novel MO-VB Scheme for Excitation Gaps in Correlated Mode Hamiltonians Correlated Approach to Molecular Properties Infinite Volume Extrapolations of Finite Clusters Calculations - How Correct are These? Calculation of the Hyperpolarisabilities of Organic Molecules and their Role in the Interpretation of Nonlinear Optical Phenomena in Organic Crystals Energy Thresholds in Polysilanes - Elementary Excitations of Alternating Conjugated Chains Inter- and Intramolecular Spin Coupling in Organics Electron Correlation Effects in Semiconductorquantum Dot Nanostructures Numerical Simulations of Strongly-Correlated Systems-Interlayer Tunnelling Mechanism, Spin-Charge Separation and Odd-Gap Pairing Metal Insulator Transition in 3rd Transition Metal Oxides Superconductivity in Doped Fullerenes.