相关论文: HyperDiamond Feynman Checkerboard in 4-dimensional…

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of…

We present a theory of lattice-enriched semirings, called quantic semirings, which generalize both quantales and powersets of hyperrings. Using these structures, we show how to recover the spectrum of a Krasner hyperring (and in particular,…

This thesis is concerned with the development of a general method to compute renormalised local observables for quantum matter fields, in a given quantum state, on a rotating black hole spacetime. The rotating black hole may be surrounded…

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R4 and R6. Furthermore, we construct some integrable and…

Harmonic superspaces for spacetimes of dimension $d\leq 3$ are constructed. Some applications are given.

In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain…

We survey and develop the most elementary model of electron motion introduced by R$.$Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional…

We consider conformal four-point Feynman integrals to investigate how much of their mathematical structure in two spacetime dimensions carries over to higher dimensions. In particular, we discuss recursions in the loop order and spacetime…

We report on the observation of anti-ferromagnetic correlations of ultracold fermions in a variety of optical lattice geometries that are well described by the Hubbard model, including dimers, 1D chains, ladders, isolated and coupled…

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this…

The class of non-commutative hypercomplex number systems (HNS) of 4-dimension, constructed by using of non-commutative Grassmann-Clifford procedure of doubling of 2-dimensional systems is investigated in the article and established here are…

We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…

We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state…

In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrise-type diagrams. Applications are shown along with basic concepts and…

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a…

We study the phase diagram of two models of spin-1/2 antiferromagnets composed of corner-sharing tetrahedra, the basis of the pyrochlore structure. Primarily, we focus on the Heisenberg antiferromaget on the checkerboard lattice (also…

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-$T_c$ cuprates, iron pnictides, and heavy-fermion compounds. A new approach to this most fundamental and…

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$…

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Boltzmann (LB) construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function (EDF) are addressed. A…

The successful emulation of the Hubbard model in optical lattices has stimulated world wide efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics. Unfortunately, for bosons,…