18 citations · 114 across the 22 of their papers we have counts for
23 papers
Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles
Arkadiusz Bochniak, Shinsei Ryu, Jürgen Fuchs +1
Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conject…
On Geometric Spectral Functionals
Arkadiusz Bochniak, Ludwik Dąbrowski, Andrzej Sitarz +1
We investigate spectral functionals associated with Dirac and Laplace-type differential operators on manifolds, defined via the Wodzicki residue, extending classical results for Di…
An impediment to torsion from spectral geometry
Arkadiusz Bochniak, Ludwik Dąbrowski, Andrzej Sitarz +1
Modifications of standard general relativity that bring torsion into a game have a long-standing history. However, no convincing arguments exist for or against its presence in phys…
Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
Arkadiusz Bochniak, Gerardo Ortiz
Starting from Halperin multilayer systems we develop a hierarchical scheme that generates, bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling f…
Quantum Mycielski Graphs
Arkadiusz Bochniak, Paweł Kasprzak
The classical Mycielski transformation allows for constructing from a given graph the new one, with an arbitrarily large chromatic number but preserving the size of the largest cli…
Spectral interactions between strings in the Higgs background
Arkadiusz Bochniak, Andrzej Sitarz
We derive the exact form of the spectral interaction of two strings mediated by a constant scalar field using methods derived from noncommutative geometry. This is achieved by cons…
Towards modified bimetric theories within non-product spectral geometry
Arkadiusz Bochniak
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetri…
Spectral interaction between universes
Arkadiusz Bochniak, Andrzej Sitarz
We derive a perturbative formula for the direct interaction between two four-dimensional geometries. Based on the spectral action principle we give an explicit potential up to the…
Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids
Arkadiusz Bochniak, Zohar Nussinov, Alexander Seidel +1
Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the…
Study of a lattice 2-group gauge model
Arkadiusz Bochniak, Leszek Hadasz, Piotr Korcyl +1
Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum…
Bosonization of Majorana modes and edge states
Arkadiusz Bochniak, Błażej Ruba, Jacek Wosiek
We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice…
Quantum correlations on quantum spaces
Arkadiusz Bochniak, Paweł Kasprzak, Piotr M. Sołtan
For given quantum (non-commutative) spaces and we study the quantum space of maps from to .…
Spectral action and the electroweak -terms for the Standard Model without fermion doubling
Arkadiusz Bochniak, Paweł Zalecki, Andrzej Sitarz
We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows…
Dynamics of a lattice 2-group gauge theory model
Arkadiusz Bochniak, Leszek Hadasz, Piotr Korcyl +1
We study a simple lattice model with local symmetry, whose construction is based on a crossed module of finite groups. Its dynamical degrees of freedom are associated both to links…
On stability of Friedmann-Lemaître-Robertson-Walker solutions in doubled geometries
Arkadiusz Bochniak, Andrzej Sitarz
Motivated by the models of geometry with discrete spaces as additional dimensions we investigate the stability of cosmological solutions in models with two metrics of the Friedmann…
Dynamical generalization of Yetter's model based on a crossed module of discrete groups
Arkadiusz Bochniak, Leszek Hadasz, Błażej Ruba
We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge tran…
Riemannian Geometry of a Discretized Circle and Torus
Arkadiusz Bochniak, Andrzej Sitarz, Paweł Zalecki
We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus ove…
Constraints of kinematic bosonization in two and higher dimensions
Arkadiusz Bochniak, Blazej Ruba, Jacek Wosiek +1
Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a g…
Bosonization based on Clifford algebras and its gauge theoretic interpretation
Arkadiusz Bochniak, Błażej Ruba
We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms o…
Pseudo-Riemannian Structures in Pati-Salam models
Arkadiusz Bochniak, Thomas E. Williams, Paweł Zalecki
We discuss the role of the pseudo-Riemannian structure of the finite spectral triple for the family of Pati-Salam models. We argue that its existence is a very restrictive conditio…
A spectral geometry for the Standard Model without the fermion doubling
Arkadiusz Bochniak, Andrzej Sitarz
We propose a simple model of noncommutative geometry to describe the structure of the Standard Model, which satisfies spin condition, has no fermion doubling, does not lead t…
Finite Pseudo-Riemannian Spectral Triples and The Standard Model
Arkadiusz Bochniak, Andrzej Sitarz
Starting from the formulation of pseudo-Riemannian generalisation of real spectral triples we develop the data of geometries over finite-dimensional algebras with indefinite metric…
Braided Hopf algebras from twisting
Arkadiusz Bochniak, Andrzej Sitarz
We show that a class of braided Hopf algebras, which includes the braided is obtained by twisting. We show further examples and demonstrate that twisting of bicovariant d…