A toy model shows that cosmic topology alters the bound-state energy of a 3D Dirac delta potential by a coefficient C_Γ=6 for the 3-torus and C_Γ=4 for the half-turn space, suppressed by exp(-L/g_R).
Renormalized Path Integral in Quantum Mechanics
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abstract
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.
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Probing the Universe's Topology through a Quantum System?
A toy model shows that cosmic topology alters the bound-state energy of a 3D Dirac delta potential by a coefficient C_Γ=6 for the 3-torus and C_Γ=4 for the half-turn space, suppressed by exp(-L/g_R).