2011/10/06 by В. В. Варламов, V. V. Varlamov, Varlamov, V. V.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #gr-qc #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1110.1146
32 pages
arxiv created 2011/10/06 · openalex publication_date 2011/10/06 · arxiv updated 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extended particles are considered in terms of the fields on the Poincaré group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincaré group. Free fields of the spin 1/2 and 1 (Dirac and Maxwell fields) are considered in detail on the eight-dimensional homogeneous space, which is equivalent to a direct product of Minkowski spacetime and two-dimensional complex sphere. It is shown that a massless spin-1 field, corresponding to a photon field, should be defined within principal series representations of the Lorentz group. Interaction between spin-1/2 and spin-1 fields is studied in terms of a trilinear form. An analogue of the Dyson formula for S-matrix is introduced on the eight-dimensional homogeneous space. It is shown that in this case elements of the S-matrix are defined by convergent integrals.