Hopf maps and Wigner's little groups

Abstract

We present the explicit formulae relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed.

9pp, published version

References in corpus (15)

• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• Superparticle Models with Tensorial Central Charges
• BPS states in M-theory and twistorial constituents
• A note on quantum Bohlin transformation
• Four-dimensional Hall mechanics as a particle on $\DC P^3$
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
• The Seven-sphere and its Kac-Moody Algebra
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• Introduction to Division Algebras, Sphere Algebras and Twistors
• Elements of (super-)Hamiltonian Formalism
• 3D Oscillator and Coulomb Systems reduced from Kahler spaces
• Brane Content of Branes' States
• Little Groups of Preon Branes

Cited by in corpus (5)

• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8
• Magic Coset Decompositions
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• Reductions related with Hopf maps