Quaternionic Quantum Mechanics and Quantum FieldsThis book signals a major conceptual advance in quaternionic quantum mechanics; significant results from earlier literature, together with many new ones obtained by the author, are integrated to give a coherent picture of the subject. |
Contents
NONRELATIVISTIC QUATERNIONIC QUANTUM MECHANICS | 87 |
RELATIVISTIC QUATERNIONIC QUANTUM MECHANICS | 301 |
Appendix A Proof of the Jacobi Identity for the Generalized Poisson Bracket | 535 |
Appendix B Derivation of Gaussian Integral Formulas | 541 |
| 553 | |
| 563 | |
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Common terms and phrases
adjoint analogous analysis angular momentum anti-self-adjoint operator anticommutes asymptotic bosonic canonical cluster coefficients commute complex quantum mechanics conjugation construction coordinate representation corresponding covariant d³x denote derivative Dirac equation eigenstates eigenvalue energy eigenstates equation of Eq factors formally real gauge invariant gauge potential gauge transformation given in Eq gives H₁ Hamiltonian Heisenberg picture Hence Hilbert space implies independent inner product integral Klein-Gordon Lagrangian densities left-acting algebra linear Lorentz matrix elements momentum operator multiparticle nionic nonrelativistic octonionic operator gauge invariant particle perturbation phase Poincaré Poincaré group properties quantum field theory quater quaternion algebra quaternion imaginary quaternionic field quaternionic Hilbert space quaternionic quantum mechanics ray representative S-matrix scalar Schrödinger equation self-adjoint solutions spinor standard structure Substituting Eq symmetry symplectic components time-independent tion total trace Lagrangian vanishes vector wave function zero