相关论文: Introduction to p-adic q-difference equations (wea…
Using the theory of pro-p groups and relative Poincar\'{e} duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of…
The paper has the form of a proposal concerned with the relationship between the three mathematically rigorous approaches to quantum field theory: 1) local algebraic formulation of Haag, 2) Wightman formulation and 3) the perturbative…
In this work, we explore both the ordinary $q$-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the $q$-deformed diffusion differential equation. This…
We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We then apply this to constructively test if solutions of linear q-difference…
Let $\mathbb{F}_q$ be a finite field of order $q$. Iosevich and Rudnev (2005) proved that for any set $A\subset \mathbb{F}_q^d$, if $|A|\gg q^{\frac{d+1}{2}}$, then the distance set $\Delta(A)$ contains a positive proportion of all…
For transcendental functions that solve non-linear $q$-difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin and infinity. We describe such solutions of a $q$-discrete…
We establish a generalization of the p-adic local monodromy theorem (of Andre, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called fake annuli. The latter…
In this work we study global boundedness and exponential integrability of weak solutions to degenerate $p$-Poisson equations using an iterative method of De Giorgi type. Given a symmetric, non-negative definite matrix valued function $Q$…
As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum…
A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on…
In this paper, we use two $q$-operators $\mathbb{T}(a,b,c,d,e,yD_x)$ and $\mathbb{E}(a,b,c,d,e,y\theta_x)$ to derive two potentially useful generalizations of the $q$-binomial theorem, a set of two extensions of the $q$-Chu-Vandermonde…
The Weak approximation theorem describes the closure of $G(Q)$ inside $G(Q_p)$ as well as inside $G(R)$ for $G$ an algebraic group over $Q$; the closure is always an open normal subgroup with finite abelian quotient, and is well understood…
The straightforward description of q-deformed systems leads to transition amplitudes that are not numerically valued. To give physical meaning to these expressions without introducing {\it ad hoc} remedies, one may exploit an "internal"…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
The discrete Fourier transform has proven to be an essential tool in many geometric and combinatorial problems in vector spaces over finite fields. In general, sets with good uniform bounds for the Fourier transform appear more `random' and…
A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…
In this work we establish local limit theorems for q-multinomial and multiple Heine distributions. Specifically, the pointwise convergence of the q-multinomial distribution of the first kind, as well as for its discrete limit, the multiple…
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. I also cover some important classes of applications: electron-positron…
We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universes-from-nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…