Talks

We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.

Physical theories ought to be built up from colloquial notions such as ’long bodies’, ’energetic sources’ etc. in terms of which one can define pre-theoretic ordering relations such as ’longer than’, ’more energetic than’. One of the questions addressed in previous work is how to make the transition from these pre-theoretic notions to quantification, such as making the transition from the ordering relation of ’longer than’ (if one body covers the other) to the notion of how much longer. In similar way we introduce dynamical notions ’more impulse’ (if in a collision one object overruns the other) and ’more energetic’ (if the effect of one source exceeds the effect of the other). In a physical model - built by coupling congruent standard actions - those basic pre-theoretic notions become measurable. We derive all (classical and relativistic) equations between basic physical quantities of Energy,  Momentum and Inertial Mass and ultimately the principle of least action.

Weak values were introduced by Aharonov, Albert, and Vaidman 25 years ago, but it is only in the last 10 years that they have begun to enter into mainstream physics. I will introduce weak values as done by AAV, but then give them a modern definition in terms of generalized measurements. I will discuss their properties and their uses in experiment. Finally I will talk about what they have to contribute to quantum foundations.