Polynomial KP and BKP τ-Functions and Correlators

Lattices of polynomial KP and BKP τ -functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions, are expressed via generalizations of Jacobi’s bialternant formula for Schur functions and Nimmo’s...

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Bibliographic Details
Published in:	Annales Henri Poincaré Vol. 22; no. 9; pp. 3025 - 3049
Main Authors:	Harnad, J., Orlov, A. Yu
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-09-2021 Springer Nature B.V
Subjects:	Classical and Quantum Gravitation Correlators Dynamical Systems and Ergodic Theory Elementary Particles Functions (mathematics) Lattices Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Original Paper Physics Physics and Astronomy Polynomials Quantum Field Theory Quantum Physics Relativity Theory Theoretical
Online Access:	Get full text
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Summary:	Lattices of polynomial KP and BKP τ -functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions, are expressed via generalizations of Jacobi’s bialternant formula for Schur functions and Nimmo’s Pfaffian ratio formula for Schur Q -functions. These are obtained by applying Wick’s theorem to fermionic vacuum expectation value representations in which the infinite group element acting on the lattice of basis states stabilizes the vacuum.
ISSN:	1424-0637 1424-0661
DOI:	10.1007/s00023-021-01046-z