2005/03/10 by Paul Korbel, Korbel, Paul
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.hep-th/0503092
openalex publication_date 2005/03/10 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant\ndifferential equation capable to describe relativistic particle with mass and\ninternal space-time structure. By making use of new variables that\ndifferentiate between space-time particle position and its space-time\nseparations, one finds this wave equation to become separable and providing the\ntwo kinds of solutions endowed with different physical meanings. The first kind\nconstitutes the running waves that represent Klein-Gordon-like particle. The\nsecond kind, widely discussed by Kim and Noz [4], constitutes standing waves\nwhich are normalizable space-time wave functions. To fully appreciate how\nvaluable theses solutions are it seems necessarily, however, to verify a\ngeneral outlook on relativity issue that (still) is in force. It was explained\n[5] that Lorentz symmetry should be perceived rather as the symmetry of\npreferred frame quantum description (based on the freedom of choice of\ncomparison scale) than classical Galilean idea realized in a generalized form.\nCurrently we point to some basic consequences that relate to solutions of\nFeynman equation framed in the new approach. In particular (i) Lorentz symmetry\ngroup appears to describe energy-dependent geometry of extended quantum objects\ninstead of relativity of space and time measure, (ii) a new picture of\nparticle-wave duality involving running and standing waves emerges, (iii)\nspace-time localized quantum states are shown to provide a new way of\ndescription of particle kinematics, and (iv) proposed by Witten [14]\ngeneralized form of Heisenberg uncertainty relation is derived and shown be the\nintegral part of overall non-orthodox approach.\n