Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.
We extend the representation frame formalism, previously introduced to account for key cosmological observations in the Einstein static universe, to non-relativistic quantum mechanics. In this framework, each inertial observer is associated with a flat representation referential Robs, defined as the tangent space to the spatial manifold at the observer’s position, in which all measurements are represented. The Euclidean structure of Robs allows quantum systems to be described using the standard Schrödinger formalism, avoiding the technical ambiguities that arise when quantising directly on curved manifolds. We derive the relation between the Hamiltonian governing quantum dynamics in Robs and its counterpart defined on the physical manifold U, and show that curvature effects enter as observer-dependent modifications of effective potentials. Although the resulting quantum description depends on the observer’s representation frame, we show that this does not lead to contradictions between observers: consistency of measurement outcomes follows from the standard structure of quantum correlations established by physical interactions. We illustrate the formalism with explicit applications, including the hydrogen atom in an Einstein static universe and quantum systems in the vicinity of a black hole, highlighting how spacetime curvature manifests itself in the observer’s quantum description.
We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugovecki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We concentrate on the quantum transport law in the bundle, specifically on the information which can be obtained from the flat space limit. We give a detailed proof that quantum transport coincides with parallel transport in the bundle in this limit, confirming statements of Prugovecki. Furthermore, we show that the quantum-geometric propagator in curved spacetime proposed by Prugovecki, yielding a Feynman path integral-like formula involving integrations over intermediate phase-space variables, is Poincaré gauge-covariant (i.e. is gauge-invariant except for transformations at the endpoints of the path) provided the integration measure is interpreted as a `contact point measure' in the soldered stochastic phase-space bundle raised over curved spacetime.
Abstract Single-particle physics focuses on the behavior and properties of individual particles, providing insight into the building blocks of quantum mechanics. The theory of quantum particles in curved spacetime has been getting attention in recent years for gaining a deeper understanding of the relationship between quantum mechanics and general relativity, the two pillars of modern physics. In this note, we show how single quantum particles can obtain classical behavior. In particular, for a quantum particle that follows the Klein–Gordon equation in curved spacetime in the presence of external potential, we show that when the amplitude of its wavefunction follows the Klein–Gordon equation with an arbitrary effective mass, empty curved spacetime, but with the same curved geometry appearing in the original Klein–Gordon equation of the wavefunction, the quantum force of the particle vanishes, providing a classical description of the quantum particle using a system of coupled classical equations. The result relies on the Madelung hydrodynamical reformulation of quantum mechanics. Understanding how quantum systems transition to a classical behavior is a long-standing challenge in mesoscopic physics, with important implications for a wide range of applications, from quantum computing to condensed matter physics. The result provides a fresh perspective on the relations between quantum and classical effects in curved spacetime.
Abstract Quantum coherence is a basis-dependent resource whose operational meaning becomes particularly subtle when quantum fields are observed from non-inertial reference frames or propagate through curved spacetime. In relativistic settings, the distinction between particles, modes, and accessible subsystems depends on the observer, while gravitational or accelerated horizons can restrict portions of the field from direct measurement. These effects imply that coherence assigned to one set of field modes need not coincide with that reconstructed by another observer. The problem becomes more intricate under non-stationary relativistic conditions, where acceleration, spacetime geometry, or mode structure changes with time and no single global decomposition into positive- and negative-frequency components remains universally preferred. This study develops a conceptual framework for analysing observer-dependent quantum coherence in such environments. The discussion combines quantum field theory in curved spacetime, the Unruh and Hawking effects, relativistic quantum information, and the resource-theoretic description of quantum coherence. Curved-spacetime field theory establishes that the concept of a particle is not generally observer independent [1]. Algebraic and geometric formulations further demonstrate that physically meaningful observables can remain well defined even when global particle interpretations become ambiguous [2]. Resource theory provides a complementary language for distinguishing coherence intrinsic to a chosen state representation from changes caused by observer-dependent mode decomposition [7]. Particular attention is given to accelerated observers, horizons, Bogoliubov mode mixing, time-dependent acceleration, dynamically changing accessibility of field sectors, and the distinction between genuine decoherence and redistribution of coherence into inaccessible degrees of freedom. Non-stationary relativistic motion is treated as a dynamical source of basis change rather than merely a perturbation of a stationary accelerated frame.
Abstract Quantum coherence is a fundamental resource underlying interference, entanglement-assisted processes, quantum information transfer, and the operational distinction between classical and quantum states. In laboratory-scale systems, coherence is commonly analysed relative to approximately inertial observers and weak gravitational environments. A more complete description becomes necessary when quantum systems are considered in accelerated reference frames, strong gravitational fields, or curved spacetime geometries. Under such conditions, the definition of particles, field modes, temporal evolution, and observable quantum correlations can depend on the observer and on the spacetime structure used to describe the system. This article examines the conceptual and physical behaviour of relativistic quantum coherence in non-inertial frames and curved spacetime environments without relying on a formulation based on explicit mathematical expressions. Particular attention is given to accelerated observers, horizon-related mode restrictions, observer-dependent vacuum descriptions, gravitational frequency shifts, field localization, and the transformation of accessible quantum information. Coherence is treated not merely as an intrinsic property of an isolated microscopic object but as a relational quantity affected by the physical decomposition of a quantum field into operationally accessible degrees of freedom. The analysis distinguishes coherence degradation from fundamental destruction of quantum information and emphasizes the role of inaccessible field sectors, measurement limitations, and observer-dependent subsystem definitions. Curved spacetime is further considered as a structured environment capable of modifying mode propagation, phase relationships, and correlations without behaving as a conventional material reservoir. The discussion establishes a conceptual framework relevant to relativistic quantum information, quantum field theory in non-inertial settings, gravitational quantum sensing, and future experiments involving quantum systems operating across different gravitational potentials or accelerated trajectories. The resulting perspective indicates that quantum coherence remains meaningful in relativistic physics only when the observer, field decomposition, measurement procedure, and spacetime geometry are specified consistently.
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.