Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
I will review relativistic quantum theory that is based on Wigner\'s unitary representations of the Poincare group, Dirac\'s forms of dynamics, and Newton-Wigner\'s definition of the position operator. Formulas will be derived that transform particle observables between different inertial reference frames. In the absence of interactions, these formulas coincide with Lorentz transformations from special relativity. However, when interaction is turned on, some deviations appear.
TBA
This talk presents some recent results in renormalizable noncommutative quantum field theory. After introducing the renormalization group approach in the commutative setting I will procede to its generalization to the simplest noncommutative model, $phi_4^{star 4}$ on the Moyal space. The well known phenomenon of ultraviolet/infrared mixing is cured by adding a harmonic potential term to the free action. Under the new renormalization group, adapted to the noncommutative geometry, this model turns out to be renormalizable to all orders in perturbation theory.
What does a fractional quantum Hall liquid and Kitaev\'s proposals for topological quantum computation have in common? It turns out that they are physical systems that exhibit degenerate ground states with properties seemingly different than ordinary (Landau-type) vacua, such as the ground states of a Heisenberg magnet. For example, those (topologically quantum ordered)states cannot be characterized by (local) order parameters such as magnetization. How does one characterize this new order?
The theory of Quantum Mechanics requires \'completeness\', that is, we need to know the complete set of physically allowed states before we can reliably compute quantum mechanical amplitudes. Among these possible states are microscopic black holes, since they are valid solutions to Einstein\'s equations for the gravitational force. However, a quantum description of black holes requires a drastic revision of our notions of space and time, in particular if we were to accept the interpretation of their microstates as given by superstring theories.
Wigner-Dirac relativistic quantum theory is applied to decay laws of an unstable particle in different reference frames. It is shown that decay slows down from the point of view of the moving observer, as expected. However, small deviations from Einstein\'s time dilation formula are also found. The origin of these deviations is discussed, as well as possibilities for their experimental detection.
At first sight, the ERG does not sit well with gauge theories: a naive implementation of the momentum cutoff central to the ERG breaks gauge invariance. However, things are not as they seem. Not only is it possible to construct a gauge invariant cutoff, but it is possible to construct manifestly gauge invariant ERGs. I will discuss the formulation, what has been achieved to date, and what can reasonably be hoped for in the future.
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