Related papers: Fermionic integrable models and graded Borchers tr…
In view of the obstacles encountered in any attempts to solve the Minkowski-space Bethe-Salpeter equation for bound states of two fermions, we study the possibility to model the bound-state features, at least at a qualitative level, by a…
The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted…
We realize the fundamental representations of quantum algebras via the supersymmetric Higgs mechanism in gauge theories with 8 supercharges on an $\Omega$-background. We test our proposal for quantum affine algebras, by probing the Higgs…
We introduce a fermionic formula associated with any quantum affine algebra U_q(X^{(r)}_N). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to…
We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite abelian groups. This property says that if an observable…
We study the ground-state properties of a class of $\mathbb{Z}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the…
Starting from a given factorizing S-matrix $S$ in two space-time dimensions, we review a novel strategy to rigorously construct quantum field theories describing particles whose interaction is governed by $S$. The construction procedure is…
We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
Electromagnetic fields are quantized in manifestly covariant way by means of a class of reducible representations of CCR. $A_a(x)$ transforms as a Hermitian four-vector field in Minkowski four-position space (no change of gauge), but in…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
Answering whether quantum computers can efficiently simulate quantum field theories has both theoretical and practical motivation. From the theoretical point of view, it answers the question of whether a hypothetical computer that utilizes…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
Scalar QFT on the boundary $\Im^+$ at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory is…
A deformation technique, known as the warped convolution, takes quantum fields in Minkowski spacetime to quantum fields in noncommutative Minkowski space-time. Since a quantum field is an operator valued regular distribution and the warped…