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We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
We discuss the hints for the disappearance of continuum space and time at microscopic scale. These include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory of gravity. We discuss how these ideas…
We argue that the origin of unitarity violation and information loss paradox in our understanding of black holes (BH) lies in the standard way of doing quantum field theory in curved space-time (QFTCS), which is heavily biased on intuition…
It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on…
We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a…
A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by complexifying the ghost fields and flowing…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
At the heart of quantum many-body physics lies the understanding of mechanisms that avoid quantum thermalization in an isolated system quenched far from equilibrium. A prominent example is Hilbert space fragmentation, which has recently…
The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
A set of $n$ coherent states is introduced in a quantum system with $d$-dimensional Hilbert space $H(d)$. It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
Non-Hermitian (NH) quantum systems host exceptional points (EPs), where eigenstates and eigenvalues coalesce, leading to unconventional many-body phenomena absent in Hermitian systems. While NH fermionic systems with complex interactions…