Related papers: On the algebraic approach to solvable lattice mode…
In part I: We find a series physical scales such as 1) Planck scale, 2) Minimal approximate grand unification SU(5), 3) the mass scale of the see saw model right handed or Majorana neutrinoes, some invented scale with many scalar bosons,…
An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…
We study quantum chromodynamics (QCD) on a finite lattice $\Lambda$ in the Hamiltonian approach. First, we present the field algebra ${\mathfrak A}_{\Lambda}$ as comprising a gluonic part, with basic building block being the crossed product…
We obtain the equation of state of interacting alpha matter and the critical temperature of Bose-Einstein condensation of alpha particles within an effective scalar field theory. We start from a non-relativistic model of uniform alpha…
Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…
We define and study a lattice model which we argue is in the universality class of the $OSp(2S+2|2S)$ supercoset sigma model for a large range of values of the coupling constant $g_\sigma^2$. In this first paper, we analyze in details the…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice $L$ is well-founded if and only if $K(L)$,…
We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to, the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory, and deduce the related…
The AdS/CFT correspondence has provided new and useful insights into the nonperturbative regime of strongly coupled gauge theories. We construct a class of models meant to mimic Yang-Mills theory using the superpotential method. This method…
We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product…
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
We build the trigonometric solutions of the Yang-Baxter equation that can not be obtained from quantum groups in any direct way. The solution is obtained using the construction suggested recently from the rational conformal field theory…
The virtues of resolvent algebras, compared to other approaches for the treatment of canonical quantum systems, are exemplified by infinite systems of non-relativistic bosons. Within this framework, equilibrium states of trapped and…
The light-cone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through…
Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$…
This work aims at providing new bounds for the diversity multiplexing gain trade-off of a general class of division algebra based lattice codes. In the low multiplexing gain regime, some bounds were previously obtained from the high…