2008/04/01 by Yi‐Fang Chang, Yi-Fang Chang, Chang, Yi-Fang · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0804.0267
6 pages
arxiv created 2008/04/01 · openalex publication_date 2008/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities, etc.) of bosons and fermions may be unified. On the one hand, the mathematical characteristic of particles is proposed: bosons correspond to real number, and fermions correspond to imaginary number, respectively. Such fermions of even (or odd) number form bosons (or fermions), which is just consistent with a relation between imaginary and real number. The imaginary number is only included in the equations, forms, and matrixes of fermions. It is connected with relativity. On the other hand, the unified forms of supersymmetry are also connected with the statistics unifying Bose-Einstein and Fermi-Dirac statistics, and with the possible violation of Pauli exclusion principle; and a unified partition function is obtained. Therefore, one of the possible developments is the higher dimensional complex space.