The general tensorial form of the orbit–orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off–diagonal matrix elements with respect to configurations, in a uniform way. Some special cases are shown for which the orbit–orbit interaction operator reduces to simple form. The importance of different contribut...

We summarise applications of Dyson-Schwinger equations to the theory and phenomenology of hadrons. Some exact results for pseudoscalar mesons are highlighted with details relating to the U A (1) problem. We describe inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass. We recapitulate upon studies of nucleon electromagnet...

We calculate the light-cone wave functions for QCD Fock components in a transverse virtual photon necessary applications at next-to-leading order (NLO) coupling, including quark masses. present detailed calculation of both one-loop function quark-antiquark component and tree-level quark-antiquark-gluon component. The masses are renormalized pole mass scheme, satisfying constraints from requirem...

Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12 096 distinct copies of Mermin’s magic pentagram. Remarkably, 12 096 is also the number of automorphisms of the smallest split Cayley hexagon. We give a few solid arguments showing that this may not be a mere coincidence. These arguments are mainly tied to the structure of cert...

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyse proton magnetic form factor data obtained electron+proton scattering $Q^2 \in [0.027,0.55]\,$GeV$^2$ with the goal of determining radius. The approach avoids assumptions about function used for and ensuing extrapolation onto $Q^2\simeq 0$ extraction slope. In this way, find $r_M = 0...

Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators we discuss the Bose description of the Pauli spin operators firstly proposed by Shigefumi Naka, and derive another new bosonic representation of Pauli operators. The eigenvector of σ− in the bosonic representation is a nonlinear coherent state with the eigenvalues being the Grassmann numbers.

Lately, there has been a renewed interest in fermionic one-body reduced density matrices and their restrictions beyond the Pauli principle. These are usually quantified using polytope of allowed, ordered eigenvalues such matrices. Here, we prove that this polytope’s volume rapidly approaches predicted by principle as dimension space grows additional corrections, caused generalized constraints, ...

From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional ...

We present analytical expressions for the current-current correlation function in graphene for arbitrary frequency, wavevector, doping, and band gap induced by a mass term. In the static limit we analyze the Landau (orbital) and Pauli magnetization, as well as the Lindhard correction which describes Friedel and RKKY oscillations. In the nonrelativistic limit we compare our results with the situ...