On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions
arXiv:hep-th/0604018 · doi:10.1016/j.physleta.2006.12.041
Abstract
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
arXiv comment19 pages, including 2 figures. The title and abstract were changed to more accurately reflect the content. The text was rearranged into sections, with several equations and multiple paragraphs added for clarity; and a few typos were corrected. The central equations and concepts remain unchanged.
References in corpus (22)
- Particle production and complex path analysis
- Gravity and the Thermodynamics of Horizons
- Singular Potentials and Limit Cycles
- Renormalization in Quantum Mechanics
- Renormalization of the Inverse Square Potential
- Near-Horizon Conformal Structure of Black Holes
- Quantum Anomaly in Molecular Physics
- Anomaly in conformal quantum mechanics: From molecular physics to black holes
- Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach
- The Renormalization Group Limit Cycle for the 1/r^2 Potential
- Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory
- (2+1)-Dimensional QED with Dynamically Massive Fermions in the Vacuum Polarization
- Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
- Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. II: Rotational Invariance
- On the limit cycle for the 1/r^2 potential in momentum space
- Renormalization in conformal quantum mechanics
- Dynamical chiral symmetry breaking in gauge theories with extra dimensions
- Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics
- Scattering from Singular Potentials in Quantum Mechanics
- D-Branes and their Absorptivity in Born-Infeld Theory
- Effective Field Theory Program for Conformal Quantum Anomalies
- Power-law singularities in string theory and M-theory
Cited by in corpus (11)
- Renormalization of Singular Potentials and Power Counting
- Polymer quantization, singularity resolution and the 1/r^2 potential
- Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential
- On Robin boundary conditions and the Morse potential in quantum mechanics
- Singular inverse-square potential: renormalization and self-adjoint extensions for medium to weak coupling
- Point-Particle Effective Field Theory II: Relativistic Effects and Coulomb/Inverse-Square Competition
- Renormalization of the strongly attractive inverse square potential: Taming the singularity
- Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
- J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory
- J-matrix method of scattering for potentials with inverse square singularity: The real representation
- Multichannel Framework for Singular Quantum Mechanics