2009/07/31 by S. I. Kruglov, S I Kruglov · 21 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Covariant Hamiltonian field theory #Eigenvalues and eigenvectors #Formalism (music) #Hamiltonian (control theory) #Klein–Gordon equation #Lagrangian #Maxwell's equations #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Schrödinger equation #Wave equation #gr-qc #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/43/24/245403
published in Journal of Physics A Mathematical and Theoretical 43(24), 245403 (Institute of Physics) · 17 pages, minor corrections, published version
arxiv created 2010/05/25 · openalex publication_date 2010/05/25 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau–Duffin–Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy–momentum and spin projections are obtained, and we find the density matrix for the massive state. The 13 × 13-matrix Schrödinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.