Path Integral Junctions
High Energy Physics - Theory
2012-06-06 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
We propose path integral description for quantum mechanical systems on compact graphs consisting of N segments of the same length. Provided the bulk Hamiltonian is segment-independent, scale-invariant boundary conditions given by self-adjoint extension of a Hamiltonian operator turn out to be in one-to-one correspondence with N \times N matrix-valued weight factors on the path integral side. We show that these weight factors are given by N-dimensional unitary representations of the infinite dihedral group.
Cite
@article{arxiv.1201.5115,
title = {Path Integral Junctions},
author = {Satoshi Ohya},
journal= {arXiv preprint arXiv:1201.5115},
year = {2012}
}
Comments
13 pages, 14 figures; typos corrected, references added, discussion of weight factors improved