Qiss

This paper shows that the generalization of the Barnich-Troessaert bracket recently proposed to represent the extended corner algebra can be obtained as the canonical bracket for an extended gravitational Lagrangian. This extension effectively allows one to reabsorb the symplectic fluinto the dressing of the Lagrangian by an embedding field. It also implies that the canonical Poisson bracket of charges forms a representation of the extended corner symmetry algebra.

I describe two phenomenological windows on quantum gravity that seem promising to me. I argue that we already have important empirical inputs that should orient research in quantum gravity.

We shed some light on the reason why the accidental flatness constraint appears in certain limits of the amplitudes of covariant loop quantum gravity. We show why this constraint is harmless, by displaying how analogous accidental constraints appear in transition amplitudes of simple systems, when certain limits are considered.

The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first recall the definition of Yutsis diagrams, a standard graphical calculus used in quantum chemistry and quantum gravity, which captures the main features of SU(2) representation theory. Second, we show precisely how it embed within Penrose’s binor calculus. Third, we subsume both calculus into ZXH-diagrams. In the process we show how the SU(2) invariance of Wigner symbols is trivially provable in the ZXH-calculus. Additionally, we show how we can explicitly diagrammatically calculate 3jm, 4jm and 6j symbols. It has long been thought that quantum gravity should be closely aligned to quantum information theory. In this paper, we present a way in which this connection can be made exact, by writing the spin-networks of loop quantum gravity (LQG) in the ZX-diagrammatic language of quantum computation.

It is frequently stated that the electromagnetic vector potential acquires a fundamental role in quantum physics, whereas classically it only represents a convenient, but by no means necessary, way of representing the electromagnetic field. Here we argue that this is a historical accident due to the fact that the electromagnetic field was discovered before photons, while the electron itself was discovered first as a particle, before it became clear that it must also be treated as a wave and therefore as an excitation of the underlying electron field. We illustrate the fact that the vector potential ought to play a fundamental role classically using the Aharonov-Bohm effect. This effect is considered as the strongest argument for the role the vector potential plays in quantum physics, however, here we offer a fully classical account of it. This is a consequence of the fact that any account, be it classical or quantum, must involve the vector potential in order to preserve the local nature of the Aharonov-Bohm (as well as all the other) phases.

We study the superposition of primordial massive particles and compute the associated decoherence time scale in the radiation dominated universe. We observe that for lighter primordial particles with masses up to $10^7,rm{kg}$, the corresponding decoherence time scale is significantly larger than the age of the observable universe, demonstrating that a primordial particle would persist in a pure quantum state, with its wavefunction spreading freely. For heavier particles, they can still be in a quantum state while their position uncertainties are limited by the wavelength of background photons. We then discuss three observational signatures that may arise from a quantum superposition of primordial particles such as primordial black holes and other heavy dark matter candidates, namely, interference effects due to superpositions of the metric, transition lines in the gravitational wave spectrum due to gravitationally bound states indicating the existence of gravitons, and witnesses of quantum entanglement between massive particles and of the gravitational field.

Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous proposals could yield reversible transformations between arbitrary quantum reference frames only when applied to the whole universe. In contrast, here we derive quantum reference frame transformations from first principles, using only standard quantum theory. Our framework, naturally based on incoherent rather than coherent group averaging, yields reversible transformations that only depend on the reference frames and system of interest. We find more general transformations than those studied so far, which are valid only in a restricted subspace. Importantly, our framework contains additional degrees of freedom in the form of an “extra particle,” which carries information about the quantum features of reference frame states. Our formalism is valid for a broad range of symmetry groups. We study the centrally extended Galilei group specifically, highlighting key differences from previous proposals.

The formalism of quantum theory over discrete systems is extended in two significant ways. First, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. Second, quantum evolutions are generalized to act over network configurations, in such a way that nodes be allowed to merge, split and reconnect coherently in a superposition. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.