**Cong Zhang, Univ. Warsaw/Beijing**

**Title: Some analytical results about the Hamiltonian operator in LQG**

PDF of the talk (1.7M)

Audio+Slides [.mp4 10MB]

by Jorge Pullin, LSU

One of the central elements when building quantum theories using the approach known as "canonical" is to define a quantity known as the Hamiltonian. This quantity is responsible for the time evolution of the system under study. In general relativity, when one tries to construct such quantity one notices it vanishes. This is because in general relativity one can choose any arbitrary time variable and therefore there is not a uniquely selected evolution. One needs to make a choice. One such choice is to use matter to play the role of a clock. That leads to one having a non-vanishing Hamiltonian. In this work a detailed construction for the quantum operator associated with such Hamiltonian in loop quantum gravity was presented. The implementation presented differs from others done in the past. Among the attractive elements is that it can be shown in certain circumstances that the operator has the desirable mathematical property known as "self-adjointness". This property ensures that physical quantities in the theory are represented by real (as opposed to complex) numbers.

A discussion was also presented of how the operator acts on certain states that behave semi-classically known as "coherent states", in particular in the context of cosmological models. It was observed that it leads to an expanding universe.