Related papers: Prescriptions for measuring and transporting local…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…
Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with…
When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric.…
We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum…
We study the momentum space representation of energy-momentum tensor two-point functions on a space with a planar boundary in $d=3$. We show that non-conservation of momentum in the direction perpendicular to the boundary allows for new…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…
We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study…
In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product…
Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies we assume that the metric of momentum space determines the condition of on-shellness while the…
The general notion of anisotropic connections $\nabla$ is revisited, including its precise relations with the standard setting of pseudo-Finsler metrics, i.e., the canonic nonlinear connection and the (linear) Finslerian connections. In…
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
In general relativity the parallel transfer of a vector around a closed curve in spacetime, or along two curves which together form a closed loop, usually results in a nonzero deficit angle between the vector's initial and final positions.…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
We show that the $\kappa$-Poincar\'e Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality \cite{AFKS}. We study the geometric properties of the momentum space described by…
We discuss the observability of a one-dimensional Schr\"odinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we…
The disagreement between low- and high-redshift measurements of the Hubble parameter is emerging as a serious challenge to the standard model of cosmology. We develop a covariant cosmographic analysis of the Hubble parameter in a general…
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…