Related papers: Zero-Energy Fields on Complex Projective Space
In this paper a framework is introduced to remove the huge discrepancy between the empirical value of the cosmological constant and the contribution to the cosmological constant predicted from the vacuum energy of quantum fields. An extra…
A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper…
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and…
A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this…
We calculate the effects of quantum fluctuations of a scalar field in the "ballpoint pen" cosmic string geometry. Using the approach to renormalization established previously for the energy density in two space dimensions, we extend those…
We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…
Gravitational waves from merging compact objects provides the opportunity to explore the properties of black holes and neutron stars in the strong regime of gravity. It is therefore of interest to explore the theoretical model that…
The heat kernel or Bargmann-Segal transform on a noncompact Riemannian symmetric space X=G/K maps a square integrable function on X to a holomorphic function on the complex crown. In this article we determine the range of this transform.
We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a…
The free energy due to the vacuum fluctuations of matter fields on a classical gravitational background is discussed. It is shown explicitly how this energy is calculated for a non-minimally coupled scalar field in an arbitrary…
In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular…
We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray…
A new method to visualize the curvature of spacetime was recently proposed. This method finds the eigenvectors of the "electric" and "magnetic" components of the Weyl tensor and, in analogy to the field lines of electromagnetism, uses the…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
Empirical studies on the landscape of neural networks have shown that low-energy configurations are often found in complex connected structures, where zero-energy paths between pairs of distant solutions can be constructed. Here we consider…
We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zero-dimensionality are shown to be equivalent. The part of this characterisation that…
We discuss exact scalar field solutions describing gravitating compact objects in the Eddington-inspired Born-Infeld gravity (EiBI), a member of the class of (metric-affine formulated) Ricci-based gravity theories (RBGs). We include a…
In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for…
We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our…