1934/01/01 by P. Jordan, J. v. Neumann, E. P. Wigner · 4 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Applications #Advanced Mathematical Theories and Applications #Noncommutative and Quantum Gravity Theories #Mathematics #Formalism (music) #Algebraic number #Quantum #Generalization #Algebra over a field #Pure mathematics #Quantum mechanics #Mathematical analysis #Physics
paper · doi:10.2307/1968117
openalex publication_date 1934/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is commutative but not associative.1 This algebra differs from the non-commutative but associative matrix algebra usually considered in that one is concerned with the commutative expression ½(A × B + B × A) instead of the associative product A × B of two matrices. It was conjectured that the laws of this commutative algebra would form a suitable starting point for a generalization of the present quantum mechanical theory. The need of such a generalization arises from the (probably) fundamental difficulties resulting when one attempts to apply quantum mechanics to questions in relativistic and nuclear phenomena.