Related papers: Explicit Implicit Function Theorem for All Fields
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie…
We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the…
There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series…
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…
This paper develops explicit class field theory for orders: of rank 1 in any global function field -- Hayes theory -- and of rank 2 in real quadratic function fields -- Real Multiplication. The essential ingredient in the development of the…
We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.
The recent method of the description of classical fields in terms of Lagrange-Souriau form is applied to the case of source-free electromagnetic field in order to check its computational capabilities. The relevant calculations are…
We prove an implicit function theorem for non-commutative functions. We use this to show that if $p(X,Y)$ is a generic non-commuting polynomial in two variables, and $X$ is a generic matrix, then all solutions $Y$ of $p(X,Y)=0$ will commute…
We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over…
Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article we introduce Hilbertian fields and present a clear detailed proof of Hilbert's irreducibility theorem in the context of these fields.
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
We illustrate how effective field theories work in nuclear physics by using an effective Lagrangian in which all other degrees of freedom than the nucleonic one have been integrated out to calculate the low-energy properties of two-nucleon…
A planar tree power series over a field $K$ is a formal expression $$\sum c_T \cdot T$$ where the sum is extended over all isomorphism classes of finite planar reduced rooted trees $T$ and where the coefficients $c_T$ are in $K$.…
The main result of the work ``The nilpotence conjecture in K-theory of toric varieties'' is extended to all coefficient fields of characteristic 0, thus covering the class of genuine toric varieties.
In this talk I review an effective field theory that has been developed for processes with energetic hadrons, referred to as the Soft-Collinear Effective Theory. After outlining properties of the effective theory I briefly discuss its…
In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a…
We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.
Consider an arbitrary complex-valued, twice continuously differentiable, nonvanishing function $\phi$ defined on a finite segment $[a,b]\subset \mathbb{R}$. Let us introduce an infinite system of functions constructed in the following way.…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We determine an explicit triangular integral basis for any separable cubic extension of a rational function field over a finite field in any characteristic. We obtain a formula for the discriminant of every such extension in terms of a…