Relativistic Hamiltonian dynamics of singularities of the Liouville equation. (English) Zbl 0539.35068
Summary: A constraint Hamiltonian description of the dynamics of singularities (regarded as point particles) is given for a previously considered class of solutions of the Liouville equation in two space-time dimensions. Reparametrization invariant Newton like equations are written down for the N-particle motion. The corresponding phase space Hamiltonian approach is formulated in terms of asymptotic particle coordinates and momenta. In the 2-particle case interpolating canonical coordinates are introduced in the Markov-Yukawa gauge (in which \((q_ 1-q_ 2)(p_ 1+p_ 2)=0)\), thus making contact with current formulation of relativistic particle dynamics. The relation between (non-canonical) physical position variables and the corresponding velocities on one hand and asymptotic canonical coordinates and momenta on the other is also established in the 2-particle case.
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35A20 | Analyticity in context of PDEs |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
Keywords:
Hamiltonian description; dynamics of singularities; Liouville equation; Markov-Yukawa gaugeReferences:
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