Related papers: Issues in Quantum-Geometric Propagation
We show that spinors propagating in curved gravitational background acquire an interaction with spacetime curvature, which leads to a quantum mechanical geometric effect. This is similar to what happens in the case of magnetic fields, known…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a…
We use a full general relativistic framework to study the self-similar expansion of bubbles of the stable phase into a flat Friedmann-Lema\^itre-Robertson-Walker Universe in a first order phase transition in the early Universe. With a…
In previous work, a lattice scalar propagator was rigorously defined in $d=1$ flat space and shown to equal the known Klein-Gordon propagator of QFT. This work generalizes this lattice propagator to manifolds whose universal cover is the…
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a…
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
This letter serves as the generalization of the work 2505.16436, where we investigated the quantum field theory in Klein space which has two time directions. We extend studies to the general spacetime $\mathbb{R}^{n,d-n}\,(n,d-n\geq2)$ in a…
A recently-developed theory of quantum general relativity provides a propagator for free-falling particles in curved spacetimes. These propagators are constructed by parallel-transporting quantum states within a quantum bundle associated to…
We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
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…
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,…
Many homogeneous, four-dimensional space-time geometries can be considered within real projective geometry, which yields a mathematically well-defined framework for their deformations and limits without the appearance of singularities.…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with…