Presented By: Department of Mathematics
Bessel operators as toy models of renormalization group
Jan Derezinski (University of Warsaw)
In Quantum Field Theory one usually needs to perform the following steps:
1. Cut off the formal Hamiltonian with a momentum cutoff.
2. Add an appropriate counterterm times a running coupling constant.
3. Determine the differential equation for the coupling constant.
4. Go with the cutoff to infinity.
I will show that the same steps are needed in the much simpler context of Bessel Hamiltonians, that is, Schr\"odinger operators with the inverse square potential, if you use the momentum representation. The action of scaling on self-adjoint realizations of Bessel operators serves as a nice illustration of a "renormalization group flow".
1. Cut off the formal Hamiltonian with a momentum cutoff.
2. Add an appropriate counterterm times a running coupling constant.
3. Determine the differential equation for the coupling constant.
4. Go with the cutoff to infinity.
I will show that the same steps are needed in the much simpler context of Bessel Hamiltonians, that is, Schr\"odinger operators with the inverse square potential, if you use the momentum representation. The action of scaling on self-adjoint realizations of Bessel operators serves as a nice illustration of a "renormalization group flow".
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