Related papers: Zero-Energy Fields on Complex Projective Space

We introduce a three-dimensional random point field using the concept of the quaternion determinant. Orthogonal polynomials on the space of pure quaternions are defined, and used to construct a kernel function similar to the Ginibre kernel.…

We consider gauge theories based on abelian $p-$forms on real compact hyperbolic spaces. Using the zeta-function regularization method and the trace tensor kernel formula, we determine explicitly an expression for the vacuum energy (Casimir…

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…

Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.

In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the…

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…

In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp…

Let $(M,g)$ be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of $f$ along maximal geodesics vanish on an appropriate open subset of the space of geodesics…

All fiber bundle with a given set of characteristic classes are viewable as particular projections of a more general bundle called a universal classifying space. This notion of projector valued field, a global definition of connections and…

We present two constructions of projective systems of measures associated to discretizations of free scalar Euclidean quantum fields. The first one is obtained using only purely combinatorial data and applies to free massless scalar fields…

The equivalence between rank-2 anti-symmetric tensor fields, considered as gauge potentials, and torsionless non-linear $\sigma$-models suggests us to study the possibility of coupling tensorial matter with Yang-Mills fields, through the…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

We define a complex horospherical transform for affine symmetric spaces of Hermitian type and show that it has no kernel on the holomorphic discrete series.

In this paper we study the attenuated $X$-ray transform of 2-tensors supported in strictly convex bounded subsets in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical $X$-ray data. The…

A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable:…

In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…

We discuss properties of the index hypergeometric transform (it is named also the Jacobi transform or the Olevsky transform) interpolating analysis of Berezin kernels on rank 1 symmetric spaces. We discuss a unitary intertwining operator…

A new type of gauge quantum theory (superrelativity) has been proposed. This differs from ordinary gauge theories in sense that the affine connection of our theory is constructed from first derivatives of the Fubini-Study metric tensor.…

We describe a full-field coherent imaging approach suitable for hard X-rays based on a classical (i.e. Galilean) X-ray microscope. The method combines a series of low-resolution images acquired at different transverse lens positions into a…

Using thermal quantization of geodesics confined under horizons and reasonable conjecture on massless modes, we evaluate quantum spectrum of Kerr black hole masses compatible with superstring symmetries.