The recently proposed construction approach to nonperturbative QFT, based on modular localization, is reviewed and extended. It allows to unify black holes physics and H-temperatures (H standing for Hawking or Horizon) with the bootstrap-formfactor program for nonperturbative construction of low dimensional QFT. In case of on-shell particle number conservation, the equations characterizing the ...

We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories. The central ingredient is a special Frobenius algebra object A in the modular category that encodes the Moore--Seiberg data of the underlying chiral CFT. Just ...

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

Three dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be “twisted”, in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized ...

Among several ideas which arose as consequences of modular localization there are two proposals which promise to be important for the classification and construction of QFTs. One is based on the observation that wedge-localized algebras under certain conditions have particle-like generators with simple properties and the second one uses the structural simplification of wedge-localized algebras ...

In previous work, we have independently reasoned about developing “safe” object-oriented (OO) systems, and constructing modular safety arguments. One of the challenges currently under consideration is how to successfully certify safety-critical OO systems developed using this approach. It was concluded that in order to maintain the desirable properties of OO systems such as re-use and inheritan...

Three-dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be “twisted,” in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized ...

(1) Explicit class field theory for global function fields (just as torsion of Gm gives abelian extensions of Q, and torsion of CM elliptic curves gives abelian extension of imaginary quadratic fields). Here global function field means Fp(T ) or a finite extension. (2) Langlands conjectures for GLn over function fields (Drinfeld modular varieties play the role of Shimura varieties). (3) Modular...

Manual derivation of the dynamic model of a modular robot is almost impossible because it may have very different geometries and DOFS through module reconfiguration. This paper presents an algorithm to automatically generate the closed-form equation of motion of a modular robot from a kinematic graph based representation of the assembly configuration. We consider modular robots with the more ge...