Related papers: Fourier restriction estimates on quantum Euclidean…

We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime.…

We explore the connections between the constraints on the precision of quantum logical operations that arise from a conservation law, and those arising from quantum field fluctuations. We show that the conservation-law based constraints…

We develop the quantum field theory of fermion mixing in curved spacetime and discuss the role of unitarily inequivalent representations in the particle interpretation of the theory. We derive general oscillation formulae and apply them to…

Recent works in quantum gravity, motivated by the factorization problem and baby universes, have considered sums over bordisms with fixed boundaries in topological quantum field theory (TQFT). We discuss this construction and observe a…

In this paper we consider adjoint restriction estimates for space curves with respect to general measures and obtain optimal estimates when the curves satisfy a finite type condition. The argument here is new in that it doesn't rely on the…

The concept of a quantum structure underlying space has been proposed for quite some time, yet it has largely eluded direct observation. There is a prevailing notion that the minuscule effects stemming from quantum space could, under…

Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…

Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…

We give an alternative argument to the application of the so-called Maurey- Nikishin-Pisier factorisation in Fourier restriction theory. Based on an induction-on-scales argument, our comparably simple method applies to any compact quadratic…

Using the $ku$- and $BP$-theoretic versions of Astey's cobordism obstruction for the existence of smooth Euclidean embeddings of stably almost complex manifolds, we prove that, for $e$ greater than or equal to $\alpha(n)$--the number of…

In this article, we define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz's restriction theorem for the Fourier-Dunkl transform for a cone-hyper-surface and its generalisation to the family of…

In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive…

In the finite field setting, we show that the restriction conjecture associated to any one of a large family of $d=2n+1$ dimensional quadratic surfaces implies the $n+1$ dimensional Kakeya conjecture (Dvir's theorem). This includes the case…

Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…

A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…

In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize…

We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore…

In relativistic quantum constraint mechanics the state of a physical system is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier transformation can be used to relate this state between constraint spaces in 4-position and…

All matter is made up of fermions -- one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the…