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(Anti-)Symmetrizing Wave Functions · Around

2017

(Anti-)Symmetrizing Wave Functions

Krishnan, Chethan, Kumar, K. V. Pavan, Subramanian, P. N. Bala

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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 generic number of particles and 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 arbitrary number of flavors follows.

Built on

M. Hamermesh, “Group Theory and Its Application to Physical Problems,” Addison-Wesley Publishing Company, Inc., 1962. Z. Ma, “Group Theory for Physicists,” World Scientific Pub. Co. Ltd., 2007. A. J. Coleman, “The Symmetric Group Made Easy,” Adv. in Q.Chem 4
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D. Griffiths, “Introduction to Elementary Particles,” John Wiley and Sons, Inc., 1987
1987
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J. Fuchs and C. Schwigert, “Symmetries, Lie Algebras and Representations,” Cambridge University Press, 1997
1997
Earlier work this paper cites.
Jin-Quan Chen, Jialun Ping and Fan Wang, “Group Representation Theory for Physicists”, World Scientific, 2002
2002
Earlier work this paper cites.

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