Relativistic conic motion as a second-class dynamical system

IF 1.8 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
EPL Pub Date : 2024-06-20 DOI:10.1209/0295-5075/ad49d1
S. L. Oliveira, C. M. B. Santos and R. Thibes
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引用次数: 0

Abstract

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.
作为二等动力系统的相对论圆锥运动
我们以狄拉克-贝格曼约束动力学模型为基础,研究了在开放势能影响下沿着一般圆锥路径的相对论运动。结果发现,该系统在相空间中表现出一组四个二等约束,我们通过相对论泊松代数对之前已知的代数结构进行了全面探索。利用方便的积分因子,欧拉-拉格朗日微分方程就能以闭合形式求出通解。我们运用狄拉克-伯格曼算法,对相应的狄拉克括号进行规范量化。我们明确得到了相空间中完整的狄拉克括号代数,以及它在微分算子方面的物理实现。
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来源期刊
EPL
EPL 物理-物理:综合
CiteScore
3.30
自引率
5.60%
发文量
332
审稿时长
1.9 months
期刊介绍: General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.
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