Related papers: The Hydra-k partial fields
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8, 6.11. These errors have been corrected in the present version of this paper. There are also some minor changes in the introduction.
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is,…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a…
Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
We discuss the importance of using partially quenched theories with three degenerate quarks for extrapolating to QCD, and present some relevant results from chiral perturbation theory.
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a…
We present some new mathematical tools which help to derive information about the quark mass matrices directly from experimental data and to elucidate the structure of these mass matrices.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We prove Hardy-type inequalities for a fractional Dunkl--Hermite operator which incidentally give Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use $h$-harmonic expansions to reduce the problem in the…
In this paper, by the tools of circulant matrices and hyperelliptic curves over finite fields, we study some arithmetic properties of certain determinants involving the Legendre symbols and $k$-th residues.
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
These notes provide three contributions to the (well-established) representation theory of Dynkin and Euclidean quivers. They should be helpful as part of a direct approach to study representations of quivers, and they may shed some new…