Related papers: Lectures on the fourth order Q curvature equation
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime…
We provide a survey of the current state of the study of diagonals of operators, especially selfadjoint operators. In addition, we provide a few new results made possible by recent work of M\"uller-Tomilov and Kaftal-Loreaux. This is an…
An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum…
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the…
We give Harnack inequalities for solutions of equations of type prescribed scalar curvature in dimensions n $\ge$ 4.
We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime curvature agrees with the renormalized volume of such domains…
In this article, we give a brief survey of recent developments on relations between global embeddability of a closed strictly pseudoconvex CR manifold and the CR Paneitz operator.
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
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 the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…
The issue of Lorentz fine-tuning in effective theories containing higher-order operators is studied. To this end, we focus on the Myers-Pospelov extension of QED with dimension-five operators in the photon sector and standard fermions. We…
Current phenomenological studies of jet observables at colliders are clearly limited by the theoretical uncertainties inherent in the next-to-leading order QCD description. We discuss the recent progress made towards the calculation of QCD…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
We relate the complexity of both differential and $q$-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too. In this…
In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.
Quantum algebra of differential operators are studied