April 2021

We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is quantized, but also the evanescent sector, with the correct physical vacuum. This yields for the first time a description of the quanta of the evanescent field alone. The key tool is the novel $alpha$-K”ahler quantization prescription based on a $*$-twisted observable algebra. The spatial evolution of states between timelike hyperplanes is established and turns out to be non-unitary if different choices are made for the quantization ambiguity for initial and final hyperplane. Nevertheless, a consistent notion of transition probability is established also in the non-unitary case, thanks to the use of the positive formalism. Finally, it is shown how a conducting boundary condition on the timelike hyperplane gives rise to what we call the Casimir state. This is a pseudo-state which can be interpreted as an alternative vacuum and which gives rise to a sea of particle pairs even in this static case.

According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.

We present a fully local treatment of the double slit experiment in the formalism of quantum field theory. Our exposition is predominantly pedagogical in nature and exemplifies the fact that there is an entirely local description of the quantum double slit interference that does not suffer from any supposed paradoxes usually related to the wave-particle duality. The wave-particle duality indeed vanishes in favour of the field picture in which particles should not be regarded as the primary elements of reality and only represent excitations of some specific field configurations. Our treatment is general and can be applied to any other phenomenon involving quantum interference of any bosonic or fermionic field, both spatially and temporally. For completeness, we present the full treatment of single qubit interference in the same spirit.

We propose a model of inflation driven by the relaxation of an initially Planckian cosmological constant due to diffusion. The model can generate a (approximately) scale invariant spectrum of (adiabatic) primordial perturbations with the correct amplitudes and red tilt without an inflaton. The inhomogeneities observable in the CMB arise from those associated to the fundamental Planckian granularity that are imprinted into the standard model Higgs scalar fluctuations during the inflationary phase. The process admits a semiclassical interpretation and avoids the trans-Planckian problem of standard inflationary scenarios based on the role of vacuum fluctuations. The deviations from scale invariance observed in the CMB are controlled by the self coupling constant of the Higgs scalar of the standard model of particle physics. The thermal production of primordial black holes can produce the amount of cold dark matter required by observations. For natural initial conditions set at the Planck scale the amplitude and tilt of the power spectrum of perturbations observed at the CMB depend only on known parameters of the standard model such as the self coupling of the Higgs scalar and its mass.

ZX-calculus is graphical language for quantum computing which usually focuses on qubits. In this paper, we generalise qubit ZX-calculus to qudit ZX-calculus in any finite dimension by introducing suitable generators, especially a carefully chosen triangle node. As a consequence we obtain a set of rewriting rules which can be seen as a direct generalisation of qubit rules, and a normal form for any qudit vectors. Based on the qudit ZX-calculi, we propose a graphical formalism called qufinite ZX-calculus as a unified framework for all qudit ZX-calculi, which is universal for finite quantum theory due to a normal form for matriof any finite size. As a result, it would be interesting to give a fine-grained version of the diagrammatic reconstruction of finite quantum theory [Selby2021reconstructing] within the framework of qufinite ZX-calculus.

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes, besides super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein’s equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of GR: Gravity is a manifestation of spacetime geometry. Thus, the approach emphasizes the quantum nature of geometry and focuses on its implications in extreme regimes — near the big bang and inside black holes — where Einstein’s smooth continuum breaks down. We present a brief overview of the main ideas underlying LQG and highlight a few recent advances. This report is addressed to non-experts.