New 3D Formalism for Internal Structure of Relativistic Systems

A new three-dimensional, boost-invariant formalism has been developed to describe the internal structure of relativistic systems. This advance, based on light-front quantum mechanics, allows for the construction of invariant wave functions for constituents moving at near-light speeds. The key lies in the Miller-Brodsky variable, \tilde{z}, which is canonically conjugate to the momentum fraction x and enables a spatial description of the longitudinal degree of freedom. The researchers demonstrated how \tilde{z} can be constructed as an operator and proved its boost invariance. To illustrate its application, they used a relativistic harmonic oscillator potential, previously introduced by Li, Maris, Zhao, and Vary, as an example of a two-body interaction constructible with \tilde{z}. This model allowed for obtaining closed-form analytical solutions, facilitating the analysis of conditions under which non-relativistic harmonic oscillator solutions are reproduced and when relativistic corrections become significant. This development is particularly relevant because harmonic oscillator states are commonly used as a basis for nuclear many-body calculations. The proposed formalism could lay the groundwork for obtaining light-front wave functions of nuclei, opening new avenues for understanding the internal dynamics of nuclear matter in relativistic regimes. This work is expected to drive future research in describing relativistic quantum systems with greater precision.