Idempotents of Clifford Algebras

A classification of idempotents in Clifford algebras C(p,q) is presented. It is shown that using isomorphisms between Clifford algebras C(p,q) and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive idempotents used to generate minimal one sided ideals in Clifford algebras. Some low dimensional examples are discussed

Entanglement and Tensor Product Decomposition for Two Fermions

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not proper entanglement measure in this case. The explicit formula for the entanglement of formation is found and its dependence on tensor product decompositions of the Hilbert space is discussed. It is shown that the set of separable states is narrower than in two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.Comment: 8pp, published versio

Quantum mechanics of a free particle on a pointed plane revisited

The detailed study of a quantum free particle on a pointed plane is performed. It is shown that there is no problem with a mysterious ``quantum anticentrifugal force" acting on a free particle on a plane discussed in a very recent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we deal with a purely topological efect related to distinguishing a point on a plane. The new results are introduced concerning self-adjoint extensions of operators describing the free particle on a pointed plane as well as the role played by discrete symmetries in the analysis of such extensions.Comment: 4 figure

Measurements of π±\pi^\pm, K±^\pm, p and pˉ\bar{\textrm{p}} spectra in proton-proton interactions at 20, 31, 40, 80 and 158 GeV/c with the NA61/SHINE spectrometer at the CERN SPS

Measurements of inclusive spectra and mean multiplicities of $\pi^\pm$, K$^\pm$, p and $\bar{\textrm{p}}$ produced in inelastic p+p interactions at incident projectile momenta of 20, 31, 40, 80 and 158 GeV/c ($\sqrt{s} =$ 6.3, 7.7, 8.8, 12.3 and 17.3 GeV, respectively) were performed at the CERN Super Proton Synchrotron using the large acceptance NA61/SHINE hadron spectrometer. Spectra are presented as function of rapidity and transverse momentum and are compared to predictions of current models. The measurements serve as the baseline in the NA61/SHINE study of the properties of the onset of deconfinement and search for the critical point of strongly interacting matter

Measurement of Hadron Production in π−\pi^--C Interactions at 158 and 350 GeV/c with NA61/SHINE at the CERN SPS

We present a measurement of the momentum spectra of $\pi^\pm$, K$^\pm$, p$^\pm$, $\Lambda$, $\bar{\Lambda}$ and K$^{0}_{S}$ produced in interactions of negatively charged pions with carbon nuclei at beam momenta of 158 and 350 GeV/c. The total production cross sections are measured as well. The data were collected with the large-acceptance spectrometer of the fixed target experiment NA61/SHINE at the CERN SPS. The obtained double-differential $p$-$p_T$ spectra provide a unique reference data set with unprecedented precision and large phase-space coverage to tune models used for the simulation of particle production in extensive air showers in which pions are the most numerous projectiles

Measurements of ππ±^{±} , KK±^{±}, pp and pˉ\bar{p} spectra in proton-proton interactions at 20, 31, 40, 80 and 158 GeV/cc with the NA61/SHINE spectrometer at the CERN SPS

Measurements of inclusive spectra and mean multiplicities of π ± π± , K ± ± , p and p ¯ p¯ produced in inelastic p + p interactions at incident projectile momenta of 20, 31, 40, 80 and 158 GeV /c GeV /c (s √ = s= 6.3, 7.7, 8.8, 12.3 and 17.3 GeV GeV , respectively) were performed at the CERN Super Proton Synchrotron using the large acceptance NA61/SHINE hadron spectrometer. Spectra are presented as function of rapidity and transverse momentum and are compared to predictions of current models. The measurements serve as the baseline in the NA61/SHINE study of the properties of the onset of deconfinement and search for the critical point of strongly interacting matter

Measurement of hadron production in π–^{–}−C interactions at 158 and 350 GeV / c with NA61/SHINE at the CERN SPS

We present a measurement of the momentum spectra of π $^{±}$, K$^{±}$, p$^{±}$, Λ, $\overline{Λ}$, and K$^{0}$$_{S}$ produced in interactions of negatively charged pions with carbon nuclei at beam momenta of 158 and 350 GeV/c. The total production cross sections are measured as well. The data were collected with the large-acceptance spectrometer of the fixed target experiment NA61/SHINE at the CERN SPS. The obtained double-differential p−pT spectra provide a unique reference dataset with unprecedented precision and large phase-space coverage to tune models used for the simulation of particle production in extensive air showers in which pions are the most numerous projectiles