Unified Hamiltonian theory of relativistic particle equations

摘要: Abstract This paper discusses four related topics of the theory relativistic free particle equations. 1. I. A unified equation is derived for Zitterbewegung space coordinate. Our derivation based (besides quantum, e.g., Heisenberg motion and commutation relations which are valid in nonrelativistic also) on postulate that a square Hamiltonian equal to sum squares momentum mass. results hold also massless particles. 2. II. Using classical, Hamilton's canonical equations motion—in addition assumptions named under 1—we derive explicit structure linear (but not necessarily p!) spins 0, 1 2 , makes it particularly clear why, cases 0 1, Hermitian, contrast spin case. We see these former cases, second order momentum, again The “hidden assumption” Dirac's particles formulated explicitly: commutativity between velocity coordinate operators. 3. III. spin-dependent aspects Spinbewegung show up time-dependence hypercomplex operators represented by matrices. For case, appears its purest form, uncluttered Spinbewegung. express rotation charge space. perhaps most physical way introduction concept Dirac particle, exhibited ϱk σk where, f.i., αk = ϱ1 · β ϱ3. ordinary space, is, general, slower than characterizing Zitterbewegung. It pointed out magnetic field “averaging over Zitterbewegung” leads Pauli (in representation). (Weyl neutrino photon) coalesce corresponding takes place 4. IV. interdependence discussed. as compatibility conditions coexistence Hamilton motion. difference approach our considerations Wigner's well-known demonstration nonfollowing harmonic oscillator from classical quantum explained. Appendix very briefly other forms equations: A—Wigner-Bargmann charge-conjugation violating equations; B—Foldy “canonical” preserving C—Sakata-Taketani type quasi-unified D—Duffin-Kemmer redundant (!), 1; E—“Covariant canonical” B explains what meant an operator (matrix) meaning statement depends another b.