Generalized Fock-Lorentz Transformations from Projective Conformal Coordinates with Applications to Relativistic Oscillators
Researchers present a systematic formulation of generalized Fock-Lorentz transformations using projective conformal coordinates that induce nonlinear transformations of physical spacetime coordinates. The approach clarifies the structure of relativistic invariants and introduces a coordinate-dependent speed of light, with applications to one-dimensional relativistic quantum oscillators. This work provides a theoretical framework that may deepen understanding of relativistic quantum mechanics and could have implications for systems with position-dependent effective parameters.
The paper develops a compact mathematical formulation of generalized Fock-Lorentz transformations based on auxiliary Minkowski coordinates defined through a projective conformal map. When ordinary Lorentz transformations act linearly on these auxiliary coordinates, they induce nonlinear transformations of physical spacetime coordinates, with the deformation controlled by a length scale R and a constant vector. The authors clarify how the conformal factor relates to an effective, coordinate-dependent speed of light and derive an apparent mass that varies with position. As a concrete application, they construct symmetrized one-dimensional Klein-Gordon and Dirac oscillators in the time-like sector, showing that the energy spectra acquire explicit Fock-Lorentz corrections that smoothly reduce to standard relativistic results as the deformation length approaches infinity. The work also examines weak-gradient anharmonic effects from space-like deformations and establishes conditions for consistent quantum treatment.
What's missing
The paper does not discuss experimental signatures or observational tests that could validate or constrain the deformation parameter R, nor does it address potential connections to phenomenological models in condensed matter or high-energy physics where such coordinate-dependent effective parameters arise naturally.
What different sources said
- arXiv physicsCenter
Hyperstatistical thermodynamics of the one-dimensional Klein-Gordon and Dirac oscillators: a closed-form q-generalized Boltzmann factor and a quantitative comparison with Beck's superstatistics
- arXiv physicsCenter
Generalized Fock--Lorentz Transformations from Projective Conformal Coordinates and Their Application to One-Dimensional Relativistic Oscillators
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