Related papers: Standard and Hyperfinite Unifications for All Phys…
Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable. For X in L(A), it is known that the restriction A^X is…
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
Talk given at Frontiers in Particle Physics Conference, Cargese. In this paper, I provide some motivation for supersymmetric grand unified theories, briefly explain an extension of the standard model based on them and present a calculation…
Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry $U_q(\sg)$. Their representation theory…
The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes…
Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…
Recently it has been found that in a noncompact formulation of the SU(2) gauge theory on a lattice the physical volume is larger than in the Wilson theory with the same number of sites. In its original formulation such noncompact…
In the paper we obtain some new applications of well--known W. Rudin's theorem concerning lacunary series to problems of combinatorial number theory. We generalize a result of M.-C. Chang on L_2 (L)-norm of Fourier coefficients of a set…
W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied…
Let P be a maximal parabolic of a classical group over a field F. Then the Levi subgroup M is isomorphic to the product of a classical group and a general linear group, acting on vector spaces X and W, respectively. In this paper we…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We find the complete branching law for the restriction of certain unitary representations of $O(1,n+1)$ to the subgroups $O(1,m+1)\times O(n-m)$, $0\leq m\leq n$. The unitary representations we consider belong either to the unitary…
Unified field theories act to merge the internal symmetries of the standard model into a single group. Here we lay out something different. That is, instead of aiming to unify the internal symmetries, we demonstrate a sense in which the…
Effective theories are well established theoretical frameworks to describe the effect of energetically widely separated UV models on observables at lower energy scales. Due to the complexity of the effective theory when taking all the…
In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras…
Unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi-ordered by subsumption up to variable renaming (i.e., $t_1\preceq t_2$ iff $t_1 =…
We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…
Set theory brought revolution to philosophy of mathematics and it can bring revolution to philosophy of physics too. All that stands in the way is the intuition that sets of physical objects cannot themselves be physical objects, which…
Currently, string theory represents the only advanced approach to a unification of all interactions, including gravity. In spite of the more than thirty years of its existence it did not make any empirically testable predictions. And it is…