Dirac canonical idea as an alternative to the approach of Bohr. A toy model

Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be reasonably revisited. The outlined model indicates new issues, which could result from following and exploring the canonical idea of Dirac. Topological defects in solids are considered as an example. The aim is helping to grasp the underlying pre-theoretical new intuitions, which should replace the old ones attached to the background of classical physics.

💡 Research Summary

The paper revisits the foundations of quantum theory by challenging the Bohr‑style correspondence principle, which treats classical objects merely as passive backgrounds for quantum phenomena. Instead, it adopts Dirac’s canonical quantization as a conceptual alternative, arguing that quantum structure should be embedded directly in the canonical variables of a classical system rather than imposed a posteriori on classical trajectories. The authors begin with a historical overview, noting that since the early days of quantum mechanics classical objects have been excluded from the list of subjects that can exhibit quantum properties, a stance that recent experiments on topological defects in solids have begun to question.

The core of the work is a “toy model” built around topological defects such as dislocations, domain walls, or flux lines in crystalline media. Starting from a classical Lagrangian that includes the elastic displacement field (u(x)) and a set of Lagrange multipliers (\lambda(x)) enforcing the defect constraint (C