Living with the ghosts
Event details
| Date | 23.02.2015 |
| Hour | 14:00 |
| Speaker | Dr Andrey Smilga (Universite of Nantes) |
| Location |
Cubotron 727
|
| Category | Conferences - Seminars |
Lagrangians with higher derivatives involve "ghosts" meaning that their Hamiltonian is not bounded neither from below, nor from above. Most people think that it is a disaster and ruins the theory completely.
My point, however, is that it is not so. There is no problem whatsoever in free theory. Consider e.g. the Hamiltonian representing a difference of two usual harmonic oscillator Hamiltonians. The spectrum $E_{nm} = \omega_1(n+1/2) - \omega_2(m+ 1/2)$ does not have a bottom, but the Hilbert space is well defined and the evolution operator is unitary.
Typically, ghosts strike back when one includes interaction. One observes a collapse (the phenomenon of the same nature as falling on the center in the attractive $1/r^2$ potential) and violation of unitarity. But there are some special nontrivial interactive systems when the ghosts are "benign" and collapse does not occur. There are several QM examples and one interesting 2d field theory example.
It is not thus forbidden now to dream that a real fundamental Theory of Everything represents a higher-derivative theory living in a flat higher-dimensional bulk and our World lives on its 3-brane classical solution.
My point, however, is that it is not so. There is no problem whatsoever in free theory. Consider e.g. the Hamiltonian representing a difference of two usual harmonic oscillator Hamiltonians. The spectrum $E_{nm} = \omega_1(n+1/2) - \omega_2(m+ 1/2)$ does not have a bottom, but the Hilbert space is well defined and the evolution operator is unitary.
Typically, ghosts strike back when one includes interaction. One observes a collapse (the phenomenon of the same nature as falling on the center in the attractive $1/r^2$ potential) and violation of unitarity. But there are some special nontrivial interactive systems when the ghosts are "benign" and collapse does not occur. There are several QM examples and one interesting 2d field theory example.
It is not thus forbidden now to dream that a real fundamental Theory of Everything represents a higher-derivative theory living in a flat higher-dimensional bulk and our World lives on its 3-brane classical solution.
Practical information
- General public
- Free