Quantum Gravity

In quantum gravity, observables must be diffeomorphism-invariant. Such observables are nonlocal, in contrast with the standard assumption of locality in flat spacetime quantum field theory. I will show how to construct 'gravitationally dressed' observables in linearized gravity that become local in the weak gravity limit, and whose corrections to exact locality are characterized by the Newtonian potential. One can attempt to make these observables more local by concentrating gravitational field lines into a smaller solid angle. In AdS_3 gravity I will show that nonperturbatively there are sharp limits to how much the gravitational dressing can be concentrated.

Based on arXiv:1507.07921 with Steve Giddings, and arXiv:1510.00672 with Don Marolf and Eric Mintun.

In this talk, I will review the Refined Gribov-Zwanziger framework designed to deal with the so-called Gribov copies in Yang-Mills theories and its standard BRST soft breaking. I will show that, within this scenario, the BRST transformations are modified in the non-perturbative regime in order to be a symmetry of the model. This fact has been supported by recent lattice simulations and opens a new avenue for the investigation of non-perturbative effects in Yang-Mills theories.

In the summer of 2015, the speaker led a team at Microsoft Research, comprised primarily of research interns from seven universities, to demonstrate a social, ambulatory, Mixed Reality system for the first time.  Each intern developed a preliminary, domain-specific exploration of how such a system could be used.  One of the interns, Andrzej Banburski of the Perimeter Institute, demonstrated an interface to Mathematica.  The very concept and terminology of Virtual Reality had been first articulated by the speaker almost four decades earlier precisely in the hopes of experiencing this type of interface.  Mathematical expressions floating in the air is not just more vivid that writing them on a blackboard; a different workflow and mental framework becomes possible.  For instance, functions appear as lenses that can be compounded as they are lined up.  One can peer through a stack of such lenses at different data or starting conditions.  Instead of erasing and replacing portions of expressions on a blackboard, a stack of lenses can fork and merge, so that a range of variations can be explored at once as aspects of a sculptural form.   The purpose is not just to make math more accessible to those who might find this interface more inviting, but to free math from pre-computational, notation-bound conventions.  The speaker will argue that this type of interface, while still only barely explored, could eventually have a significant impact both on computer science and other disciplines, including theoretical physics. 

We analyse different classical formulations of General Relativity in the Batalin (Frad-
kin) Vilkovisky framework with boundary, as a first step in the program of CMR [1] quantisation. Success and failure in satisfying the axioms will allow us to discriminate among the different descriptions, suggesting that some are more suitable than others in view of perturbative quantisation. Based on a joint work with A. Cattaneo [2, 3] we will present the details of the application of the BV-BFV formalism to the Einstein-Hilbert and Palatini-Holst formulations of General Relativity. We show that the two descriptions are no longer equivalent from this point of view, and we discuss possible interpretations of this result.

[1] A. S. Cattaneo, P. Mnëv, N. Reshetikhin, Classical BV theories on manifolds with boundary, Comm. Math. Phys. 332, 2, 535-603 (2014); A.S. Cattaneo, P. Mnëv, N. Reshetikhin, Perturbative quantum gauge theories on manifolds with boundary, arXiv:1507.01221
[2] A. S. Cattaneo, M. Schiavina, BV-BFV analysis of General Relativity. Part I: Einstein Hilbert action, arXiv:1509.05762 (2015).
[3] A. S. Cattaneo, M. Schiavina, BV-BFV analysis of General Relativity. Part II: Palatini Holst action, in preparation; A. S. Cattaneo, M. Schiavina, On time, in preparation.

The Hartle-Hawking (HH) no-boundary proposal provides a Euclidean path integral prescription for a measure on the space of all possible initial conditions. Apart from  saddle point  and  minisuper-space calculations, it is hard to obtain results using the unregulated path integral. A promising choice of spacetime  regularisation comes from the causal set (CST) approach to quantum gravity.  Using analytic results as well as Markov Chain Monte Carlo and numerical integration methods we obtain  the HH wave function in a theory of non-perturbative 2d CST. We find that the  wave function is sharply peaked with the peak geometry changing discretely with "temperature". In the low temperature regime the peak corresponds to causal sets which have no continuum counterpart but exhibit physically interesting behaviour. They show a rapid spatial expansion with respect to the discrete proper time as well as  a high degree of spatial homogeneity due to extensive overlap of the causal past. While our results are limited to 2 dimensions they provide a concrete example of how quantum gravity could explain the initial conditions for our observable universe.

The kinematical framework of canonical loop quantum gravity has mostly been studied in the context of compact Cauchy slices. However many key physical notions such as total energy and momentum require the use of asymptotically flat boundary conditions (and hence non-compact slices). We present a quantum kinematics, based on the Koslowski-Sahlmann representation, that successfully incorporates such asymptotically flat boundary conditions. Based on joint work with Madhavan Varadarajan.

I will describe a proposal for a generalization of the BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. I describe the computation of canonical charges and show that the associated Ward identities are equivalent to the Cachazo-Strominger subleading soft graviton formula. Based on joint work with Alok Laddha.

An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions.

Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop.

We  will  briefly review  the  issue  of    "information loss"    during  the Hawking   evaporation of a  black hole,  and  argue that    the  quantum dynamical  reduction  theories, which  have  been  developed to  address the   measurement problem  in quantum mechanics,  possess the  elements to  diffuse the ``paradox”  at the qualitative  and  at   the  quantitative  level, leading to what  seems  to be an overall  coherent  picture.  

Although the inflationary predictions for the primordial power spectrum of    density inhomogeneities   seem  very successful, there is an obscure part in our understanding of the emergence of the seeds of cosmic   structure:  How  does  a universe which at one pint  in time is described by a  state that is fully  homogeneous and isotropic,  evolve into a state that is not,   given that the dynamics  does not  contain any  source  for the  undoing of  such symmetry?   We will  discuss  an   approach that  offers  a resolution  of the  issue  in the context of  proposals to deal  with the measurement  problem in quantum  mechanics. We will  see that the   approach  naturally  resolves the difficulties  raised  by the  lack of  observation of tensor modes.

Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.