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Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well defined operators to represent the constraints and find the physical Hilbert space formed by their…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a…
It is shown that the standard no-boundary wave function has a natural expression in terms of a Lorentzian path integral with its contour defined by Picard-Lefschetz theory. The wave function is real, satisfies the Wheeler-DeWitt equation…
We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
In previous works, we have demonstrated that the path integral for {\it real, Lorentzian} four-geometries in Einstein gravity yields sensible results in well-understood physical situations, but leads to uncontrolled fluctuations when the…
The measurement-result-conditioned evolution of a system (e.g. an atom) with spontaneous emissions of photons is well described by the quantum trajectory (QT) theory. In this work we generalize the associated QT theory from infinitely wide…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes,…
A brief review of the modern state of quantum cosmology is presented as a theory of quantum initial conditions for inflationary scenario. The no-boundary and tunneling states of the Universe are discussed as a possible source of probability…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…