Schroedinger Self-adjoint Extension and Quantum Field Theory

Abstract

We argue that the results obtained using the quantum mechanical method of self-adjoint extension of the Schrödinger Hamiltonian can also be derived using Feynman perturbation theory in the investigation of the corresponding non-relativistic field theories. We show that this is indeed what happens in the study of an anyon system, and, in doing so, we establish a field theoretical description for ``colliding anyons", {\it i.e.} anyons whose quantum mechanical wave functions satisfy the non-conventional boundary conditions obtained with the method of self-adjoint extension. We also show that analogous results hold for a system of non-abelian Chern-Simons particles.

9 pages, Plain LaTex, MIT-CTP-2329

References in corpus (7)

• Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance
• Perturbative Renormalization in Quantum Mechanics
• Non-Abelian Chern-Simons Particles and their Quantization
• Differential Regularization of a Non-relativistic Anyon Model
• Coherent State Quantization of SU(N) Non-Abelian Chern-Simons Particles
• Schrödinger Fields on the Plane with non-Abelian Chern-Simons Interactions
• Comment on Partition Function of Anyon Gas

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• Unitarity, Crossing Symmetry and Duality in the scattering of $\mathcal{N}=1$ Susy Matter Chern-Simons theories
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• Perturbation Theory for Singular Potentials in Quantum Mechanics
• Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions
• Exact Wavefunctions in a Noncommutative Field Theory
• Magnetic Moment and Perturbation Theory with Singular Magnetic Fields
• Energy-pressure relation for low-dimensional gases
• Conformal Dimensions from Topologically Massive Quantum Field Theory
• Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
• On Superconformal Anyons
• Quantum Description of Anyons: Role of Contact Terms
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Renormalization group analysis of resonantly interacting anyons
• Consistency of the Born Approximation for the spin-1/2 Aharonov-Bohm Scattering
• The Renormalization Group and Quantum Hall Edge States
• Scattering in graphene with impurities : A low energy effective theory
• The Conformal Spectrum of Non-Abelian Anyons
• Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions
• On the Nonabelian Aharonov Bohm Scattering of Spinless Particles
• Second Virial Coefficient of Anyons without Hard Core
• Non-trivial Behaviour of the Scattering Amplitude of Contact-interacting Anyons
• Exchange and exclusion in the non-abelian anyon gas
• T duality for boundary-non-critical strings
• Semiclassical Theory for Two-anyon System
• On the Three-Anyon Harmonics
• Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory