2005/08/31 by Alexey V. Golovnev, ALEXEY V. GOLOVNEV
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Canonical quantization #Codimension #Dirac (video compression format) #Dirac algebra #Dirac operator #Free particle #Geometric quantization #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Second quantization #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1142/s0219887806001326
published as International Journal of Geometric Methods in Modern Physics, Vol. 3, No. 4 (2006) 655-666 · 16 pages
arxiv created 2005/11/22 · openalex publication_date 2006/06/01 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We give an explicit operator realization of Dirac quantization of free particle motion on a surface of codimension 1. It is shown that the Dirac recipe is ambiguous and a natural way of fixing this problem is proposed. We also introduce a modification of Dirac procedure which yields zero quantum potential. Some problems of Abelian conversion quantization are pointed out.