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A unitary group formulation of many‐body theory: Diagram systematics and use of the spin shifts
Author(s) -
Mukhopadhyay Atri,
Pickup Barry T.
Publication year - 1984
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560260109
Subject(s) - unitary state , physics , irreducible representation , formalism (music) , theoretical physics , many body theory , quantum mechanics , permutation group , mathematical physics , permutation (music) , art , musical , political science , acoustics , law , visual arts
This paper shows that the spin‐shift formalism developed in B. T. Pickup and A. Mukhopadhyay [Int. J. Quantum Chem. 26 , 101 (1984)] supports a one‐component diagrammatics which has a systematics akin to that in the spin‐orbital many‐body theory. The diagrams are neither Goldstone nor Yutsis type, and characterize the chain U (2 R ) ⊃ U ( R )⊗ SU (2) on which the spin‐shift formalism is based. Accordingly, while the lines in such diagrams are labeled by the orbital indices, the diagram structure adequately reflects the irreducible representation of the group U ( R ). In this sense the paper presents a unitary group approach to the natural generalization of the usual many‐body theory for the spin‐adapted cases. A set of very simple rules is derived; their similarity with the corresponding rules in the ordinary many‐body theory and practical utility are discussed in connection with (a) matrix elements over many‐electron spin states and (b) closed‐ and open‐shell many‐body perturbation theory. A possibility of integral‐driven many‐body perturbation theory for open‐shells is indicated. Connections of this formalism with others are also discussed.