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Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is…
Quantum physics on manifolds with boundary brings novel aspects due to boundary conditions. One important feature is the appearance of localised negative eigenmodes for the Laplacian on the boundary. These can potentially lead to…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
Considerations of high energies in quantum field theories on smooth manifolds have led to generalized uncertainty principles and the possibility of a physical minimal length in quantum gravitational scenarios. In these models, the minimal…
The entanglement entropy of the integer Quantum Hall states satisfies the area law for smooth domains with a vanishing topological term. In this paper we consider polygonal domains for which the area law acquires a constant term that only…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi…
The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay,…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Quantum fluctuations in the background geometry of a black hole are shown to affect the propagation of matter states falling into the black hole in a foliation that corresponds to observations purely outside the horizon. A state that starts…
We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields. Specifically, we establish that the curvature of spacetime is directly related to the entanglement entropy of…
The significance of the quantum feature of entanglement between physical systems is investigated in the context of quantum measurements. It is shown that, while there are measurement couplings that leave the object and probe systems…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…