| Issue |
EPL
Volume 146, Number 5, June 2024
|
|
|---|---|---|
| Article Number | 54001 | |
| Number of page(s) | 6 | |
| Section | Nuclear and plasma physics, particles and fields | |
| DOI | https://doi.org/10.1209/0295-5075/ad49d1 | |
| Published online | 21 June 2024 | |
Relativistic conic motion as a second-class dynamical system
Departamento de Ciências Exatas e Naturais, UESB - Rodovia BR 415, km 03 s/n, Itapetinga, Brazil
Received: 12 April 2024
Accepted: 10 May 2024
We investigate relativistic motion along a general conic path under the influence of an open potential as a Dirac-Bergmann constrained dynamical model. The system turns out to exhibit a set of four second-class constraints in phase space which we fully explore obtaining a relativistic Poisson algebra generalizing previously known algebraic structures. With a convenient integration factor, the Euler-Lagrange differential equations can be worked out to its general solution in closed form. We perform the canonical quantization in terms of the corresponding Dirac brackets, applying the Dirac-Bergmann algorithm. The complete Dirac brackets algebra in phase space as well as its physical realization in terms of differential operators are explicitly obtained.
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