2004/10/31 by Abu M. Khan, Pierre Ramond · 32 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Contraction (grammar) #Control and Stability of Dynamical Systems #Group (periodic table) #Group theory #Linguistics #Mathematical physics #Mathematics #Petri Nets in System Modeling #Philosophy #Physics #Physics and Engineering Research Articles #Pure mathematics #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1063/1.1897663
published in Journal of Mathematical Physics 46(5) (American Institute of Physics) · 22 pages; some typos corrected
arxiv created 2005/03/04 · openalex publication_date 2005/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider how the continuous spin representation (CSR) of the Poincaré group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincaré group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j, R→∞, with j∕R fixed, where R is the Kaluza–Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inönü–Wigner contraction, with the inverse Kaluza–Klein radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the Kaluza–Klein radius fixed.