1999/07/01 by R. Vilela Mendes · 33 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Open quantum system #Quantum Mechanics and Applications #Quantum differential calculus #Quantum dissipation #Quantum dynamics #Quantum probability #Quantum process #Quantum statistical mechanics #Relativistic quantum mechanics #math-ph #math.MP
paper · pdf · doi:10.1063/1.533127
published in Journal of Mathematical Physics 41(1), 156-186 (American Institute of Physics) · 36 pages Latex, 1 eps figure
arxiv created 1999/07/01 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The algebras of nonrelativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the noncommutativity of the space–time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space–time, on quantum stochastic calculus, and on the construction of quantum fields. Some of these effects are studied in this paper.