Seminar series
Date
Mon, 20 May 2013
Time
12:00 -
13:00
Location
L3
Speaker
Philip Candelas
Organisation
Oxford
It is an old idea that the imaginary part of the nontrivial Riemann zeros s =-1/2 + iE might be related to the eigenvalues of a hermitean operator H, and so to a quantum mechanical system. Such a system has been proposed by Berry and Keating; it is a harmonic oscillator with the "wrong" signatureH=1/2(xp + px). The difficulty and interest in implementing this proposal is the need to find suitable boundary conditions, or a self adjoint extension for H, since the classical phase space orbits are hyperbolae rather than circles. I will review interesting observations of Mark Srednicki relating the ground state wave functions of the Berry Keating hamiltonian and the conventional harmonic oscillator hamiltonian to the zeta function.