Related papers: Algebraic equivalence between certain models for s…
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
The SU(2) gauge invariant Dirac-Yang-Mills mechanics of spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is…
In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are…
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the…
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire…
We determine the low-energy spectrum and the eigenstates for a two-bosonic mode nonlinear model by applying the In\"{o}n\"{u}-Wigner contraction method to the Hamiltonian algebra. This model is known to well represent a Bose-Einstein…
Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…
A simple and yet powerful approach for modeling the structure of endohedrally confined diatomic molecules is introduced. The theory, based on a u(4)+u(3) dynamical algebra, combines u(4), the vibron model dynamical algebra, with a u(3)…
We review a recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions, that can be used to generate "dynamically" a large family of curved spaces. From an algebraic viewpoint,…
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…
We investigate the Hubbard model on the anisotropic triangular lattice as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation and the ladder…
We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
A systematic Hamiltonian formulation of the Einstein-Cartan system, based on the Hilbert-Palatini action with the Barbero-Immirzi and cosmological constants, is performed using the traditional ADM decomposition and without fixing the time…
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…