Related papers: Extensions of special 3-fields
In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…
The extending structures and unified products for Zinbiel algebras are developed. Some special cases of unified products such as crossed products and matched pair of Zinbiel algebras are studied. It is proved that the extending structures…
We study the evolution of the coupled scalar and fermion fields within the classical field theory. We examine the case of N coupled fields in 1+3 dimensional space. The general expressions for the fields distributions are obtained. The…
Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued…
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…
Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field…
We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We present a non-geometric derivation of $\mathcal{N}$=1 Super Yang-Mills by focusing on the consistency of interactions that extend the free vector supermultiplet rather than assuming gauge invariance under extended symmetries. By…
We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our theories exhibit exotic global and gauge symmetries, defects with restricted mobility, and interesting dualities. Depending on…
The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging in general. We study a particular family of maximal function…
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile group as well as relating it to another limit at the level…
In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this…
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…