We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of [Phys. Rev. D 22, 1922]. Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schrödinger equation associated with a symmetric Hamiltonian. When compared to the standard Schrödinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system's center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes.
In this work, based on a recently introduced localization scheme for scalar fields, we argue that the geometry of the space-time, where the particle states of a scalar field are localized, is intimately related to the quantum entanglement of these states. More specifically, we show that on curved space-time can only be localized entangled states, while separable states are located on flat space-time. Our result goes in parallel with recent theoretical developments in the context of AdS/CFT correspondence which uncovered connections between gravity and quantum entanglement.
In previous papers I expounded non-linear Schrodingerist quantum mechanics as a solution of the Measurement Problem. Here I show that NLQM is compatible with Einstein's theory of General Relativity. The extension to curved space-times presumes adoption of "space-time wavefunctions" (sometimes called "multi-time wavefunctions") and some additional algebraic structure: a "bitensor" supplementing Einstein's metric tensor. This kind of matter may violate the Strong Energy Condition even without a mass term, possibly with implications for the formation of singularities within Black Holes.
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar curvature term in the quantum Hamiltonian. The coefficient of the latter term is known to be related to the factor ordering problem in curved space quantization. Hence, in principle, the scattering data may be used to provide an experimental resolution of the theoretical factor ordering ambiguity. To demonstrate the sensitivity required of such an experimenta…
We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin $\frac{1}{2}$ fields. A curved spacetime can be equipped with a coordinate system in which the metric component $g_{--}=0$. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector $\partial_-$ and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Mi…
We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |ψ_1>, along some spacetime path Γfrom a spacetime point x_1 to another point x_2, what will the final quantum state |ψ_2> be at point x_2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-p…
We propose a generalisation of the $T \bar{T}$ deformation to curved spaces by defining, and solving, a suitable flow equation for the partition function. We provide evidence it is well-defined at the quantum level. This proposal identifies, for any CFT, the $T \bar{T}$ deformed partition function and a certain wavefunction of 3d quantum gravity. This connection, true for any $c$, is not a holographic duality --- the 3d theory is a "fake bulk." We however emphasise that this reduces to the known holographic connection in the classical limit. Concretely, this means the deformed partition functi…
In a 4-dimensional (4D) weak field geometry governed by the linearized Einstein's equations and sourced primarily by a static, spatially localized, but otherwise arbitrary mass density $T_{00}$, it is known that the leading order tail part of the Green's functions of the minimally coupled massless scalar, Lorenz gauge photon, and de Donder gauge graviton at late times are not only time translation symmetric, but also space-translation and spherically symmetric. Only the monopole moment of the matter source is responsible for the late-time tail of the Green's functions. We provide evidence, in …
We consider two scalar fields interacting through a $χ^*χϕ^*ϕ$ term in the presence of a Reissner-Nordstrom black hole. Initially, only $χ$ particles are present. We find that the produced $ϕ$ particles are localized in a region around the black hole and have a tendency towards condensation provided that $ϕ$ particles are much heavier than the $χ$ particles. We also find that such a configuration is phenomenologically viable only if the scalars and the black hole have dark electric charges.
We investigate the validity of the assertion that eternal inflation populates the landscape of string theory. We verify that bubble solutions do not satisfy the Klein Gordon equation for the landscape potential. Solutions to the landscape potential within the formalism of quantum cosmology are Anderson localized wavefunctions. Those are inconsistent with inflating bubble solutions. The physical reasons behind the failure of a relation between eternal inflation and the landscape are rooted in quantum phenomena such as interference between wavefunction concentrated around the various vacua in th…
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, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore…
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int p_μ dx^μ / \hbar$, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the firs…
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat bot…
We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel'd twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green's operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent im…
Scalar particles--i.e., scalar-field excitations--in de Sitter space exhibit behavior unlike either classical particles in expanding space or quantum particles in flat spacetime. Their energies oscillate forever, and their interactions are spread out in energy. Here it is shown that these features characterize not only normal-mode excitations spread out over all space, but localized particles or wave packets as well. Both one-particle and coherent states of a massive, minimally coupled scalar field in de Sitter space, associated with classical wave packets, are constructed explicitly. Their en…
