2002/06/12 by Artem Starodubtsev · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algorithm #Black Holes and Theoretical Physics #Canonical quantization #Geometric quantization #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #State-transition matrix #Symmetric matrix #Theoretical physics #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1016/j.nuclphysb.2003.09.053
published in Nuclear Physics B 674(3), 533-552 (Elsevier BV) · 21 pages, no figures
arxiv created 2002/06/12 · openalex publication_date 2003/10/17 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It is shown that this model has an ordinary mechanical system evolving in time as a classical solution. But in this treatment the action principle admits a natural modification which results in algebraic relations describing quantum theory. The origin of quantization is similar to that in Adler's generalized quantum dynamics. The problem with extension of this formalism to many degrees of freedom is solved by packing all the degrees of freedom into a single matrix. The possibility to apply this scheme to field theory and to various matrix models is discussed.