Classical limit of a relativistic quantum system

Ladislav Kocis

Swagata Nandi, C. S. Shastry

Mirley K. Balasubramanya

The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional harmonic oscillator in classical, relativistic and quantum regimes. The relativistic effects are considered as perturbative, within the context of a non-relativistic quantum formalism. The transition of the relativistic quantum system to both classical relativistic and classical non-relativistic regimes is illustrated in a unified framework. Formulas for the frequency of a classical relativistic oscillator and the energy eigenvalues of the corresponding quantum oscillator for the weak relativistic case are derived. Also studied are the non-relativistic and classical limits of these formulas which provide valuable insights on the parallels between relativistic and non-relativistic systems on the one hand and between classical and quantum systems on the other.

Mai-Lin Liang, Fulin Zhang, Yuan Bing +1 more

For relativistic particles with spin-0 (satisfying the Klein-Gordon equation) and spin-1/2 (satisfying the Dirac equation) in infinitely deep potential well, matrix elements for the coordinate, momentum and the velocity operators are calculated. In the limit of large quantum numbers, these matrix elements give the corresponding classical quantities (nowbeing related quantities in special relativity) and satisfy exact classical relations. These results show that the Heisenberg correspondence principle is applicable to such relativistic systems.

Dipankar Home

V. Vilasini, Renato Renner

Understanding the interface between quantum and relativistic theories is crucial for fundamental and practical advances, especially given that key physical concepts such as causality take different forms in these theories. Bell's no-go theorem reveals limits on classical processes, arising from relativistic causality principles. Considering whether similar fundamental limits exist on quantum processes, we derive no-go theorems for quantum experiments realizable in classical background spacetimes. We account for general processes allowed by quantum theory, including those with indefinite causal order (ICO), which have also been the subject of recent experiments. Our first theorem implies that realizations of ICO processes that do not violate relativistic causality must involve the nonlocalization of systems in spacetime. The second theorem shows that for any such realization of an ICO process, there exists a more fine-grained description in terms of a definite and acyclic causal order process. This enables a general reconciliation of quantum and relativistic notions of causality and, in particular, applies to experimental realizations of the quantum switch, a prominent ICO process. By showing what is impossible to achieve in classical spacetimes, these no-go results also offer insights into how causality and information processing may differ in future quantum experiments in relativistic regimes beyond classical spacetimes.