Towards constructing one-particle representations of the deformed Poincar\'e algebra

We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate eigenstates of a complete set of commuting operators starting from the rest state. One result of this work is the fact that upon deforming to the quantum Poincar\'e algebra the rest state is split into an infinite number of states. Another result is that the energy spectrum of these states is discrete. Some curious residual degeneracy remains: there are states constructed by applying different operators to the rest state which nevertheless are indistinguishable by eigenvalues of all the observables in the algebra.Comment: 23 pages. New interpretation of the results is given: upon the deformation the rest state of Poincar\'e algebra is split into an infinite number of states with discrete energy spectrum. Title, abstract and conclusion are change

RHIC polarization for Runs 9-12

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Differential Calculus on the Quantum Superspace and Deformation of Phase Space

We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum deformation of the general linear supergroup, $GL_q(m|n)$, is studied and the explicit form for the ${\hat R}$-matrix, which is the solution of the Yang-Baxter equation, is presented. We derive the quantum-matrix commutation relation of $GL_q(m|n)$ and the quantum superdeterminant. We apply these results for the $GL_q(m|n)$ to the deformed phase-space of supercoordinates and their momenta, from which we construct the ${\hat R}$-matrix of q-deformed orthosymplectic group $OSp_q(2n|2m)$ and calculate its ${\hat R}$-matrix. Some detailed argument for quantum super-Clifford algebras and the explict expression of the ${\hat R}$-matrix will be presented for the case of $OSp_q(2|2)$.Comment: 17 pages, KUCP-4

h-deformation of GL(1|1)

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL_q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.Comment: latex file, 8 pages, minor change

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

Design and Test of a Forward Neutron Calorimeter for the ZEUS Experiment

A lead scintillator sandwich sampling calorimeter has been installed in the HERA tunnel 105.6 m from the central ZEUS detector in the proton beam direction. It is designed to measure the energy and scattering angle of neutrons produced in charge exchange ep collisions. Before installation the calorimeter was tested and calibrated in the H6 beam at CERN where 120 GeV electrons, muons, pions and protons were made incident on the calorimeter. In addition, the spectrum of fast neutrons from charge exchange proton-lucite collisions was measured. The design and construction of the calorimeter is described, and the results of the CERN test reported. Special attention is paid to the measurement of shower position, shower width, and the separation of electromagnetic showers from hadronic showers. The overall energy scale as determined from the energy spectrum of charge exchange neutrons is compared to that obtained from direct beam hadrons.Comment: 45 pages, 22 Encapsulated Postscript figures, submitted to Nuclear Instruments and Method

Spin Response Function for Spin Transparency Mode of RHIC

In the Spin Transparency (ST) mode of RHIC, the axes of its Siberian snakes are parallel. The spin tune in the ST mode is zero and the spin motion becomes degenerate: any spin direction repeats every particle turn. In contrast, the lattice of a conventional collider determines a unique stable periodic spin direction, so that the collider operates in the Preferred Spin (PS) mode. Contributions of perturbing magnetic fields to the spin resonance strengths in the PS mode are usually calculated using the spin response function. However, in that form, it is not applicable in the ST mode. This paper presents a response function formalism expanded for the ST mode of operation of conventional colliders with two identical Siberian snakes in the highly-relativistic limit. We present calculations of the spin response function for RHIC in the ST mode