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Occupation Fields
Occupation fields of loop ensembles for vertices and oriented edges are introduced and their distributions are computed, together with the variations...
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Hilbertian Fields
Various alternative proofs of the irreducibility theorem apply to other fields (including all infinite finitely generated fields). We call them...
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Conformal Vector Fields
This chapter is devoted to conformal Killing vector fields, their integrability conditions, their zeros and Lichnerowicz conjecture on...
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Frobenius Fields
The embedding property (Proposition 20.7.4) for free profinite groups is essential to the primitive recursive procedure for perfect PAC fields with...
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Knotted Fields
This book provides a remarkable collection of contributions written by some of the most accredited world experts in the modern area of Knotted...
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Fields Candidacy
To whom it may concern, This letter is to officially offer my candidacy for the Fields medal. I want you to know that I would be very honored to...
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Parallel Normal Fields
For curves \(\gamma \colon [a,b] \to \mathbb {R}^n\)...
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Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields
We describe an efficient algorithm to calculate generators of power integral bases in composites of totally real fields and imaginary quadratic...
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Non-Archimedean Fields
In this chapter, we review some facts from the theory of non-Archimedean fields that will be used in later chapters. We discuss completions, Hensel’s...
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The Classical Hilbertian Fields
Global fields and functions fields of several variables have been known to be Hilbertian for three quarters of a century. These are the “classical...
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Pseudo Algebraically Closed Fields
By Hilbert’s Nullstellensatz, algebraically closed fields are PAC. So are separably closed fields [Lan64, p. 76, Prop. 10]. Both statements are also...
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Algebraically Closed Fields
We establish a simple algebraic elimination of quantifiers procedure for the theory of algebraically closed fields. This theory is model complete...
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Affine connection, quantum theory and new fields
In a few recent manuscripts, we used the affine connection to introduce two massless scalar fields in the Einstein-Palatini action. These fields lead...
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Holonomies and Gauge Fields
Given a group N, we introduce N-connections on a graph, loop holonomies, and the associated bosonic and fermionic field. When the group is discrete,...
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A reciprocity law in function fields
We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for...
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Conservation Laws of Fractional Classical Fields
This paper presents a formulation of Noether’s theorem for fractional classical fields. We extend the variational formulations for fractional...
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Fourier diffraction theorem for the tensor fields
The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties...
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Ray Transforms of the Moments of Planar Tensor Fields
AbstractThe paper considers ray transforms of the moments of symmetric tensor fields of arbitrary rank given in the unit disk. The basic geometric...