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Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
The finite and infinite square wells are potentials typically discussed in undergraduate quantum mechanics courses. In this paper, we discuss these potentials in the light of the recent studies of the modification of the Heisenberg…
The promising solution to the strong CP problem by a Peccei-Quinn (PQ) symmetry may introduce quality and hierarchy problems, which are both relevant to Planck physics. In this paper, we study whether both problems can be explained by…
One of the predictions of quantum gravity phenomenology is that, in situations where Planck-scale physics and the notion of a quantum spacetime are relevant, field propagation will be described by a modified set of laws. Descriptions of the…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
The search for a quantum theory of gravity has been one of the main aims of theoretical physics for many years by now. However the efforts in this direction have been often hampered by the lack of experimental/observational tests able to…
Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of…
One of the most difficult questions in present-day physics concerns a fundamental theory of space, time, and matter that incorporates a consistent quantum description of gravity. There are various theoretical approaches to such a…
Axions with broken discrete shift symmetry (axion monodromy) have recently played a central role both in the discussion of inflation and the `relaxion' approach to the hierarchy problem. We suggest a very minimalist way to constrain such…
We analyse the impact of quantum gravity on the possible solutions to the strong CP problem which utilize the spontaneously broken discrete symmetries, such as parity and time reversal invariance. We find that the stability of the solution…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. $\textbf{Z}_k$, the gauge couplings of U$(1)$ gauge symmetries become weak in the limit of large $k$, as $g\to k^{-\alpha}$ with $\alpha$ a positive order 1…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought…
It has been suggested recently that in a consistent theory any Minkowski vacuum must be exactly stable. As a result, a large class of theories that in ordinary treatment would appear sufficiently long-lived, in reality make no sense. In…
The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this…
A number of different approaches to quantum gravity are at least partly phenomenologically characterized by their treatment of Lorentz symmetry, in particular whether the symmetry is exact or modified/broken at the smallest scales. For…
The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections…