Related papers: Quantifier Elimination for Valued Fields Equipped …
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…
We prove automorphy lifting theorems for 2-dimensional Galois representations of absolute Galois groups of totally real fields when the residual representation is of "exceptional" type. This exceptional case is when we are in characteristic…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…
We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime…
We present an invariant relational path-integral quantization framework for general-relativistic gauge field theories based on the Dressing Field Method. The construction implements an automatic anomaly-cancellation mechanism that…
We consider field theories that exhibit a supersymmetric Lifshitz scaling with two real supercharges. The theories can be formulated in the language of stochastic quantization. We construct the free field supersymmetry algebra with rotation…
A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.
Let $A$ be a finite-dimensional associative $k$-algebra with identity. The primary aim of this paper is to study the rationality properties of the group of all $k$-algebra automorphisms of $A$, as an affine algebraic group over an arbitrary…
The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The resulting leads to a valid affine quantization of the particle in a box field theory, which points toward…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.
We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…
It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to…