Essential Self-adjointness and Quantum Cosmology
Speaker: Abhay Ashtekar, Penn State University
Abstract: To account for what was then believed to be a static universe, Einstein introduced a positive cosmological constant $\Lambda$ in his equations of general relativity. When Hubble discovered that the universe is expanding, Einstein removed the constant, calling its introduction `the greatest blunder' of his life. However, recent observations have shown that the universe is accelerating (a discovery that, incidentally, was awarded this year's physics Nobel prize). The simplest explanation is a $\Lambda$! Interestingly, it turns out that while the operator generating dynamics in quantum cosmology is self-adjoint if $\Lambda$ is non-positive, it fails to be essentially self-adjoint precisely in the physically interesting case of positive $\Lambda$. But still dynamics appears to be quite robust with respect to the choice of the self-adjoint extension. This is puzzling from a physics perspective. The goal of the seminar will be to explain this issue and seek insight from mathematicians on this intriguing phenomenon.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm