TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.195
TI  - Monopole harmonics on $\mathbb{CP}^{n-1}$
PY  - 2023/11/14
UR  - https://www.scipost.org/SciPostPhys.15.5.195
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 195
A1  - Bykov, Dmitri
AU  - Smilga, Andrei
AB  - We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.
ER  -

@Article{10.21468/SciPostPhys.15.5.195,
	title={{Monopole harmonics on $\mathbb{CP}^{n-1}$}},
	author={Dmitri Bykov and Andrei Smilga},
	journal={SciPost Phys.},
	volume={15},
	pages={195},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.195},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.195},
}