Z1/Z2 defects in 4H-SiC

First-principles calculations are carried out on models for the Z(1)/Z(2) defects in 4H-SiC which are found in as-grown and irradiated n-type material. We show that an interstitial-nitrogen-interstitial-carbon defect is exceptionally thermally stable, bistable, and has negative-U character with donor and acceptor levels close to those attributed to the defect.     

The structure of the Z 1 Z 2 → l + l − Z 1 Z 2 amplitude process outside the born approximation framework

Resummation of the perturbative series for the amplitude of lepton pair production in nucleus-nucleus collisions is performed based on the Watson theorem and the hypothesis of infrared stability. An explicit expression for this amplitude is obtained, which is valid to within terms of the ninth order in the fine structure constant.     

Ternary Z2 × Z3 Graded Algebras and Ternary Dirac Equation

The wave equation generalizing the Dirac operator to the Z₃-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors, and is therefore invariant under the product group Z₂ × Z₂ × Z₃. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) × U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.

     

Gravitational couplings and Z2 orientifolds

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low-dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold d-planes can be understood in terms of flux quantization of the d − 3 form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on T⁶/Z₂, which is dual to F-theory on a complex 4-fold with terminal singularities.     

Z2-Graded Cocycles in Higher Dimensions

Current superalgebras and corresponding Schwinger terms in 1 and 3 space dimensions are studied. This is done by generalizing the quantization of chiral fermions in an external Yang–Mills potential to the case of a Z₂-graded potential coupled to bosons and fermions.     

Rotational vibrational energy of plane symmetrical moleculeX 2 Y 2 Z 2

The rotational vibrational energy of a plane symmetrical transform of a molecule X₂Y₂Z₂ was calculated to the second approximation, while attention was paid to the anharmonic terms of third and fourth order in the potential function, Coriolis interaction of rotation and vibration, centrifugal effects and the dependence of the rotational constants on the state of vibration.     

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z ₂ scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.     

Brane world cosmology without the Z2 symmetry

The Friedmann equation for a positive tension brane situated between two bulk spacetimes that posses the same 5D cosmological constant, but which does not posses a Z₂ symmetry of the metric itself is derived, and the possible effects of dropping the Z₂ symmetry on the expansion of our Universe are examined; cosmological constraints are discussed. We show the effect of this is an inflation-like period at very early times. The global solutions for the metric in the infinite extra dimension case are found and comparison with the symmetric case is made. We show that any brane world senario of this type must revert to a Z₂ symmetric form at late times, and hence rule out certain proposed scenarios.     

Orthomodular Posets Related to Z 2-Valued States

We study orthocomplemented posets (certain quantum logics) that possess an abundance of Z ₂-valued states. We first discuss their basic properties and, by means of examples, we illuminate intrinsic qualities of these orthocomplemented posets. We then address the problem of axiomatizability of our class of posets—a question that appears natural from the algebraic point of view. In the last section we show, as a main result, that supports of the posets endowed with symmetric difference constitute an important example of orthocomplemented posets under consideration. This result is obtained by a thorough analysis of certain types of ideals.     

Enhancement of pairwise entanglement via Z2 symmetry breaking

We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.     

Solitons on Noncommutative Orbifold T 2/Z N

Following the construction of the projection operators on T ² presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold T ²/G(G=Z _N , N=2, 3, 4, 6) which correspond to a set of solitons on T ²/Z _N in noncommutative field theory. In this way, we derive an explicit form of projector on T ²/Z ₆ as an example. We also construct a complete set of projectors on T ²/Z _N by series expansions for integral case.     

Z2-twisted fields and bosonization on Riemann surfaces

The equivalence on Riemann surfaces between one Z₂-twisted boson and two fermions having different spin structures is proved. The equivalence is shown on the partition function and on the N-point functions. We analyse the consistency between the chiral and the non-chiral definitions of the twisted vertex operator. The equivalence essentially relies upon the eighty year old Schottky-Jung identities.     

Z(2) vortices and the SU(2) string tension

Topologically determined Z(2) variables in pure SU(2) lattice gauge theory are discussed. They count the number of “vortex souls”. The high temperature expansion for the corresponding Z(2) loops is examined. They obey an area law. The coefficient of the area is shown to be equal to the string tension to all orders of the high temperature expansion. This shows that the string tension is determined by the probability distribution of the vortex souls, at least in the high temperature region. The dependence of the string tension α(β, h) on an external field h that is coupled to the Z(2) field strength is calculated to lowest order of the high temperature expansion. In this approximation, α(β, h) is determined by the free energy of a 2-dimensional Ising model in an external magnetic field $\text{1}\text{2}\text{log}\text{(β/4}\text{tanh}\text{h)}$ at an inverse temperature $\text{1}\text{2}\text{log}\text{3}\text{4}\text{π = 0.429}$.     

Gravity with Electromagnetism on M4 × Z2

In the framework of the differential calculus on discrete group, which is a realization of noncommu tative geometry, we present a Kaluza-Klein-type unified Einstein-Maxwell theory on M⁴ × Z₂. By generalizing the usual concept ofi vielbein and connection and from the generalized torsion-free condition, we obtain a gravity theory which contains tensors, vectors and scafar field.     

Z 2 monopoles in the standardSU (2) lattice gauge theory model

The standardSU(2) lattice gauge theory model without fermions may be considered as aZ ₂ model with monopoles and fluctuating coupling constants. At low temperatures β^?1 (=small bare coupling constant) the monopoles are confined.