The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere

Li, Z.; Lai, Lihai; Zhong, Yi; Liu, Q.H.

doi:10.1016/j.aop.2021.168566

Cited by 1 publication

(1 citation statement)

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“…The hypersurface Σ N −1 can be described by a constraint in the configurational space as f (x) = 0 and the equation of the surface is chosen as |∇f (x)| = 1, such that the normal vector is n ≡ ∇f (x) = e i n i . As a consequence, only the unit normal vector and/or its derivatives enter the physics equation regardless of the surface equation [11,12]. Within the above quantum conditions, there are many forms of the quantum momentum p because of the operatorordering problem in O {(n i n k , j −n j n k , i ) p k } Hermition , leading to the fact that even the proper form of the momentum and the Hamiltonian cannot be determined unless more conditions are presented [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Generally covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

Liu

Zhou

et al. 2019

Eur. Phys. J. C

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For a particle that is constrained on an (N −1)-dimensional (N ≥ 2) curved surface, the Cartesian components of its momentum in N -dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the su(2) algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion. PACS numbers: 03.65.Pm Relativistic wave equations; 04.60.Ds Canonical quantization; 04.62.+v Quantum fields in curved spacetime; 98.80.Jk Mathematical and relativistic aspects of cosmology * Electronic address: quanhuiliu@gmail.com

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