# Quantum Gravity

This series consists of talks in the area of Quantum Gravity.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## The U(N) structure of Loop Quantum Gravity

Tuesday Feb 16, 2010
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It has recently uncovered that the intertwiner space for LQG carries a natural representation of the U(N) unitary group. I will describe this U(N) action in details and show how it can be used to compute the LQG black hole entropy, to define coherent intertwiner states and to reformulate the LQG dynamics in new terms.

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## Non-critical string field theory and stochastic quantization

Wednesday Jan 27, 2010
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15 years ago Ishibashi, Kawai and collaborators developed non-critical string field theory, starting with the formalism of dynamical triangulations. The same construction can be repeated using causal dynamical triangulations, and in this case one can actually sum explicitly over all genera. The theory can be viewed as stochastic quantization of space, proper (world sheet) time playing the role of stochastic time.

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## On the Relation between Operator Constraint, Master Constraint, Reduced Phase Space, and Path Integral Quantisation, with Application to Quantum Gravity

Wednesday Dec 16, 2009
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Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. We review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints.

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## Asymptotics of the Ponzano-Regge model for handlebodies

Wednesday Dec 16, 2009
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The asymptotic formula for the Ponzano-Regge model amplitude is given for non-tardis triangulations of handlebodies in the limit of large boundary spins. The formula produces a sum over all possible immersions of the boundary triangulation in three dimensional Euclidean space weighted by the cosine of the Regge action evaluated on these immersions. Furthermore the asymptotic scaling registers the existence of flexible immersions.

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## Colored group field theory: Scaling properties and positivity

Thursday Dec 10, 2009
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The scaling analysis in the large spin limit of Feynman amplitudes for the Bosonic colored group field theory are considered in any dimension starting with dimension 4. By an explicit integration of two colors, we show that the model is positive. This formulation could be useful for the constructive analysis of this type of models.

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## Recursion relations in spin foam models

Wednesday Dec 09, 2009
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Spin foam models aim at defining non-perturbative and background independent amplitudes for quantum gravity. In this work, I argue that the dynamics and the geometric properties of spin foam models can be nicely studied using recursion relations. In 3d gravity and in the 4d Ooguri model, the topological invariance leads to recursion relations for the amplitudes. I also derive recursions from the action of holonomy operators on spin network functionals.

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## Evaporating black holes in the presence of a minimal length

Thursday Nov 26, 2009
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After implementing an effective minimal length, we will present a new class of spacetimes, describing both neutral and charged black holes. As a result, we will improve the conventional Schwarzschild and Reisner-Nordstroem spacetimes, smearing out their singularities at the origin. On the thermodynamic side, we will show how the new black holes admit a maximum temperature, followed by the SCRAM phase'', a thermodynamic stable shut down, characterized by a positive black hole heat capacity.

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## Born--Oppenheimer approximation for quantum fields on quantum spacetimes

Wednesday Nov 25, 2009
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The relation between loop quantum gravity (LQG) and ordinary quantum field theory (QFT) on a fixed background spacetime still bears many obstacles. When looking at LQG and ordinary QFT from a mathematical perspective it turns out that the two frameworks are rather different: Although LQG is a true continuum theory its Hilbert space is defined in terms of certain embedded graphs which are labeled by irreducible representations of SU(2).

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## The Feynman propagator on a causal set.

Friday Nov 13, 2009
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How sure are you that spacetime is continuous? One approach to quantum gravity, causal set theory, models spacetime as a discrete structure: a causal set. This talk begins with a brief introduction to causal sets, then describes a new approach to modelling a quantum scalar field on a causal set. We obtain the Feynman propagator for the field by a novel procedure starting with the Pauli-Jordan commutation function. The candidate Feynman propagator is shown to agree with the continuum result.

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## String field theory as a diffusing system

Wednesday Nov 11, 2009
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We review some recent results on tachyon nonperturbative solutions of the nonlocal, lowest-level, effective action of string field theory. It is shown how nonlocality is encoded in a spacetime diffusion equation and how the latter emerges from the symmteries of the full, background-independent theory.

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## RECENT PUBLIC LECTURE

### Mario Livio: Brilliant Blunders

Speaker: Mario Livio