349 citations · 1.6k across the 52 of their papers we have counts for
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Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals
Felix Finster, Niky Kamran, Moritz Reintjes
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asy…
Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
Felix Finster, Niky Kamran
It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time gives rise to a distinguished state on the algebra…
The Linear Dynamics of Wave Functions in Causal Fermion Systems
Felix Finster, Niky Kamran, Marco Oppio
The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar pro…
Separability and Symmetry Operators for Painlevé Metrics and their Conformal Deformations
Thierry Daudé, Niky Kamran, Francois Nicoleau
Painlevé metrics are a class of Riemannian metrics which generalize the well-known separable metrics of Stäckel to the case in which the additive separation of variables for the Ha…
Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principles
Felix Finster, Niky Kamran
Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex struct…
Non-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
Thierry Daudé, Niky Kamran, Francois Nicoleau
In this paper, we give some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary when the Dirichlet and Neumann data are measured on…
Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces
Thierry Daudé, Niky Kamran, François Nicoleau
In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists in the compl…
Spinors on Singular Spaces and the Topology of Causal Fermion Systems
Felix Finster, Niky Kamran
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors…
An Exact Expression for Photon Polarization in Kerr Geometry
Anusar Farooqui, Niky Kamran, Prakash Panangaden
We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer tr…
A conjecture on Exceptional Orthogonal Polynomials
David Gomez-Ullate, Niky Kamran, Robert Milson
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and J…
Causality and the conformal boundary of AdS in real-time holography
Alberto Enciso, Niky Kamran
We consider the holographic prescription problem in a (Lorentzian) AdS background, deriving from first principles the explicit formulas that relate the field at infinity with the f…
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
Thierry Daude, Niky Kamran
We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the l…
Two-step Darboux transformations and exceptional Laguerre polynomials
David Gomez-Ullate, Niky Kamran, Robert Milson
It has been recently discovered that exceptional families of Sturm-Liouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Lague…
On orthogonal polynomials spanning a non-standard flag
David Gomez-Ullate, Niky Kamran, Robert Milson
We survey some recent developments in the theory of orthogonal polynomials defined by differential equations. The key finding is that there exist orthogonal polynomials defined by…
Spinor Green's functions via spherical means on products of space forms
Alberto Enciso, Niky Kamran
We explicitly compute the Green's function of the spinor Klein-Gordon equation on the Riemannian and Lorentzian manifolds of the form , with each factor…
Exceptional orthogonal polynomials and the Darboux transformation
David Gomez-Ullate, Niky Kamran, Robert Milson
We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described Laguerre po…
Global causal propagator for the Klein-Gordon equation on a class of supersymmetric AdS backgrounds
Alberto Enciso, Niky Kamran
We analyze the Cauchy problem for the Klein-Gordon equation on the type IIB supergravity backgrounds , where is any of the Sasaki-Einstein 5-manifol…
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
David Gomez-Ullate, Niky Kamran, Robert Milson
We present two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with a…
An Extension of Bochner's Problem: Exceptional Invariant Subspaces
David Gomez-Ullate, Niky Kamran, Robert Milson
A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by droppi…
Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
Felix Finster, Niky Kamran, Joel Smoller +1
This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr m…
On form-preserving transformations for the time-dependent Schrödinger equation
Federico Finkel, Artemio Gonzalez-Lopez, Niky Kamran +1
In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schrödinger eq…
Quasi-Exactly Solvable Time-Dependent Potentials
Federico Finkel, Niky Kamran
We find exact solutions of the time-dependent Schrödinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.