Related papers: Relational Motivation for Conformal Operator Order…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
Wave--particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the…
Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…
In this paper, we analyse the Wheeler-DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
In relational quantum dynamics, evolution emerges via the correlations between some system of interest and a clock system, which plays the role of a temporal reference frame. Their combined state satisfies a Wheeler-de Witt-like constraint…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally…
Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast to the…
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
The decoherent histories approach to quantum theory is applied to a class of reparametrization invariant models, which includes systems described by the Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key step in…
Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism…
Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
When the scale factor of expansion of the universe is written as $ a(t)\equiv Ae^{\alpha(t)}$, with $A$ as some real constant and $\alpha(t)$ a real function, the gravitational action $I_G$ appears in the same form as the matter action…
From the principles of quantum cosmologies we can justify the reason for an inverse-square law for the cosmological constant with no conflict with observations. Although this general expression for $\Lambda$ is well known in the literature,…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…