Timeline for What is the spectrum of the Hamiltonian of the universe?

3 events

when toggle format	what		by	license	comment
Jun 25, 2012 at 11:41	comment	added	Arnold Neumaier		@jjcale: Of course, a Hamiltonian generally contains only very little information about a system, once it has one or more continuous degree of freedom. For example, all nonrelativistic particles in a repulsive potential have (apart from a zero-point shift) the same spectrum, and so the same spectrum as QED. Nevertheless, my description gives the answer that you had asked for. You didn't ask for all information about the universe but about the spectrum of its Hamiltonian.
Jun 24, 2012 at 18:19	comment	added	jjcale		The Hamiltonian you are describing has absolutely continuous spectrum $[0,\infty)$ with infinite countable multiplicity and is therefore unitary equivalent to $-\Delta$ acting on $L^{2}(\mathbb{R}^{2})$ . So this Hamiltonian contains almost no information and all information about the universe must be encoded in the initial state. Or another mathematical framework is needed.
Jun 24, 2012 at 10:30	history	answered	Arnold Neumaier	CC BY-SA 3.0