Regge Trajectories from the Adjoint Sector of Matrix Quantum Mechanics
This presentation explores how Matrix Quantum Mechanics reveals the emergence of Regge trajectories—linear relationships between particle mass and spin—through calculations in the adjoint sector. The authors demonstrate that discretizing and diagonalizing the Mermin-Wagner equation for quartic theory produces eigenvalue patterns that align with predictions from string theory and hadronic physics, connecting quantum matrix models to the classical physics of rotating strings.Script
Particles with spin don't just sit there. They rotate, and in string theory, their mass grows linearly with angular momentum. This paper shows that pattern emerging directly from Matrix Quantum Mechanics.
Regge trajectories describe how particle mass squared scales linearly with spin. This wasn't arbitrary: rotating relativistic strings naturally produce this relationship, and experimentalists found it in families of hadrons decades ago.
The authors took a different route to find these trajectories.
They calculated in the adjoint sector of Matrix Quantum Mechanics, discretizing the Mermin-Wagner equation for quartic theory with 36,000 matrix elements. This computational approach let them extract precise eigenvalue spectra without assuming string-like behavior in advance.
When they plotted the eigenvalues, the Regge trajectories appeared. The right panel shows that the quantity delta plus 2 root 2 forms the predicted linear relationship, confirming that quantum matrix dynamics reproduce the classical string physics result without building strings into the model.
This bridges two worlds. The authors didn't impose string theory; they let it emerge from matrix quantum mechanics. That means Regge trajectories aren't just a string property—they're a consequence of deeper quantum structure, and this approach might unlock non-perturbative calculations that traditional string methods can't reach.
Matrix models don't just describe strings—they give birth to them. Visit EmergentMind.com to explore more research and create your own video presentations.
