2012/01/31 by Satoshi Ohya · 4 citations
Mathematics · Physics and Astronomy · #Combinatorics #Graph #Hamiltonian (control theory) #Hamiltonian path #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Path integral formulation #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory in Mathematical Physics #Unitary state #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/45/25/255305
published in Journal of Physics A Mathematical and Theoretical 45(25), 255305 (Institute of Physics) · 13 pages, 14 figures; typos corrected, references added, discussion of weight factors improved
openalex publication_date 2012/05/31 · arxiv created 2012/06/04 · arxiv updated 2012/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 the self-adjoint extension of a Hamiltonian operator turn out to be in one-to-one correspondence with N × 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.