Related papers: Quantifier elimination for quasi-real closed field…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where…
It is shown that relativistic wave equations for free, massless fields display quantum-classical complementarity.
In this paper, I provide a formal set of assumptions and give a natural criterion for a quantum field theory to admit particles. I construct a na\"ive approach to localization for a free bosonic quantum field theory and show how this…
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.
Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore…
We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the \NPAz. They are made in the same spirit as the dynamic algebraic closure of a field. They give a concrete content to the theorem…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
We prove that, for countable languages, two model-theoretic quantifier elimination tests, one proposed by J. R. Shoenfield and the other by L. van den Dries, are equivalent.
The algebras of interacting "Lie random fields" that were introduced in J. Math. Phys. 48, 122302 (2007) are developed further. The conjecture that the vacuum vector defines a state over a Lie random field algebra is proved. The difference…
Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the…
We present a reduction of the function field Mordell-Lang conjecture to the function field Manin-Mumford conjecture, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for (generalized) Zariski…