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(Anti-)symmetrizing wave functions

Krishnan, C and Pavan Kumar, KV and Bala Subramanian, PN (2019) (Anti-)symmetrizing wave functions. In: Journal of Mathematical Physics, 60 (2).

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Official URL: https://doi.org/10.1063/1.5038076


The construction of fully (anti-)symmetric states with many particles, when the single particle state carries multiple quantum numbers, is a problem that seems to have not been systematically addressed in the literature. A quintessential example is the construction of ground state baryon wave functions where the color singlet condition reduces the problem to just two (flavor and spin) quantum numbers. In this paper, we address the general problem by noting that it can be re-interpreted as an eigenvalue equation and provide a formalism that applies to the generic number of particles and the generic number of quantum numbers. As an immediate result, we find a complete solution to the two quantum number case, from which the baryon wave function problem with an arbitrary number of flavors follows. As a more elaborate illustration that reveals complications not visible in the two quantum number case, we present the complete class of states possible for a system of five fermionic particles with three quantum numbers each. Our formalism makes systematic use of properties of the symmetric group and Young tableaux. Even though our motivations to consider this question have their roots in Sachdev-Ye-Kitaev-like tensor models and holography, the problem and its solution should have broader applications.

Item Type: Journal Article
Publication: Journal of Mathematical Physics
Publisher: American Institute of Physics Inc.
Additional Information: The copyright for this article belongs to the Author(s).
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 31 Oct 2022 11:25
Last Modified: 31 Oct 2022 11:25
URI: https://eprints.iisc.ac.in/id/eprint/77730

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