Six generatorq-deformed Lorentz algebra

The six generator deformation of the Lorentz algebra is presented. The Hopf algebra structure and the reality conditions are found. The chiral decomposition of SL(2, C) is generalized to theq-case. Casimir operators for theq-Lorentz algebra are given.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-85-15857.     

q-Deformed Poincaré algebra

Theq-differential calculus for theq-Minkowski space is developed. The algebra of theq-derivatives with theq-Lorentz generators is found giving theq-deformation of the Poincaré algebra. The reality structure of theq-Poincaré algebra is given. The reality structure of theq-differentials is also found. The real Laplacian is constructed. Finally the comultiplication, counit and antipode for theq-Poincaré algebra are obtained making it a Hopf algebra.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139     

Bicovariant quantum algebras and quantum Lie algebras

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun toU _q g, given by elements of the pure braid group. These operators—the reflection matrixYL ⁺ SL ^– being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation forY inSO _q (N).This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY90-21139     

Reality in the differential calculus on q-Euclidean spaces

The nonlinear reality structure of the derivatives and the differentials for the Euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-85-15857.     

String theory and loop space index theorems

We study index theorems for the Dirac-Ramond operator on a compact Riemannian manifold. The existence of a group action on the loop space makes possible the definition of a character valued index which we calculate by using a two-dimensional sigma model withN=1/2 supersymmetry. We compute the Euler characteristic, the Hirzebruch signature and the Dirac-Ramond genus of loop space. We compare our results to the calculations made by using the Atiyah-Singer character-valued index theorem.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857. Fermilab is operated by the Universities Research Association, Inc., under contract with the United States Department of Energy     

The logarithm of the derivative operator and higher spin algebras ofW ∞ type

We use the notion of the logarithm of the derivative operator to describeW type algebras as central extensions of the algebra of differential operators. We also provide closed formulae for the truncations ofW ₁₊ to higher spin algebras withsM, for allM2. The results are extended to matrix valued differential operators, introducing a logarithmic generalization of the Maurer-Cartan cocycle.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76Sf00098 and in part by the National Science Foundation under grants PHY-85-15857 and PHY-87-17155Address after July 1, 1992: Dept. of Mathematics, Yale University, New Haven, CTO6520, USA     

Graph theory,SO(n) current algebra and the Virasoro master equation

We announce an isomorphism between a set of generically irrational affine-Virasoro constructions onSO(n) and the unlabelled graphs of ordern. On the one hand, the conformal constructions are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. High-level expansion provides a strong argument that each construction is unitary down to some finite critical level.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857     

A construction of thec<1 modular invariant partition functions

Decomposition theorems for certain representations of Kac-Moody algebras which are needed for the construction of modular invariant unitary conformal models are proved. It is shown that allc<1 modular invariant models can then be recovered from gauged free fermionic models, including the exceptional cases.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857Supported by the Swiss National Science FoundationSupported in part by the American-Israeli Binational Science Foundation and the Israeli Academy of Sciences     

Braided Hopf algebras and differential calculus

We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross-product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139.Supported in part by a Feodor-Lynen Fellowship.     

Mind,matter, and quantum mechanics

A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between:(1) mind and matter,(2) quantum theory and reality,(3) relativity theory and becoming, and (4) relativity theory and Bell's theorem.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract W-7405-EN-G-48.     

Super-Kac-Moody algebras and supersymmetric 2d-free fermions

Explicit representations of super-Kac-Moody algebra are constructed in terms of 2d-free fermions which form a non-linear representation of supersymmetry with the fermions grouped with the generators of the algebra into superfields. It is shown how the most general construction of this type corresponds to homogeneous spacesG/H and how supersymmetry alone is responsible for that structure.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contracts DE-AC03-76SF00098     

Some nonabelian toy models in the largeN limit

Schwinger-Dyson equations are used to study the largeN limit ofU(N) gauge theory on several small lattices. Explicit solutions are found which are beyond the reach of existing steepest descent technique. They show a phase transition in a three placquette model at couplingg ² N=3, resembling the known transition in the one placquette model, and lending support to expectations of a similar transition in the four dimensional lattice theory.This work was supported in part by the High Energy Physics Division of the U.S. Department of Energy under contract No. W-7495-ENG-48     

Beta-delayed two-proton decay of39Ti

The beta-delayed two-proton decay of theT _z =–5/2 nuclide³⁹Ti has been observed. The³⁹Sc isobaric analog state has been calculated to lie at 8.82 MeV using the measured two-proton sum energy of 4750±40 keV for its decay to the³⁷K ground state. Combining this excitation energy with a Coulomb displacement energy calculation has lowered the energy available for ground state two-proton emission of³⁹Ti from 760 to 530 keV.This work was supported by Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Depeartment of Energy under Contracts DE-AC03-76SF00098 with Lawrence Berkeley Laboratory, DE-AC02-76CH00016 with Brookhaven National Laboratory and DE-AC06-76RL0 1830 with Pacific Northwest Laboratories.     

Algebraic study of chiral anomalies

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of descent equations.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under research grant PHY81-18547     

Topological representations of the quantum groupU q(sl 2)

We define a topological action of the quantum groupU _q(sl ₂) on a space of homology cycles with twisted coefficients on the configuration space of the punctured disc. This action commutes with the monodromy action of the braid groupoid, which is given by theR-matrix ofU _q(sl ₂).Currently visiting the Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA. Supported in part by the NSF under Grant No. PHY89-04035, supplemented by funds from the NASA     

Probing new physics from top-charm associated productions at Linear Colliders

Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phasespace form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the no-growth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization. This work was supported in part by the Director, Office of Energy Research Office of High Energy and Nuclear Physics, Division of High Energy Physics of the US Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under Research Grant No. PHY-85-15857. The work of Z. Bern was also supported by the Danish Research Council     

Comment on the7Li(p, γ)8Be reaction at energies of astrophysical interest

The results of two recent publication are reconsidered. These papers argue that the p-wave effects seen in the⁷ Li(p, ) ⁸ Be reaction belowE _p=80 keV can be accounted for by considering the low-energy tail of the p-wave resonance atE _p=441 keV. It is shown that the cross section and analyzing power data require an order-of-magnitude more p-wave strength when considered together.This work was supported by the U.S. Department of Energy, Office of High Energy and Nuclear Physics, under Contract No. DEFG05-91-ER40619.     

Large-xF spin asymmetry inπ0 production by 200-GeV polarized protons

The spin asymmetryA _N for inclusive ⁰ production by 200-GeV transversely-polarized protons on a liquid hydrogen target has been measured at Fermilab over a wide range ofx _F, with 0.5p _T<2 gev/c.=">x _F>0.3, the asymmetry rises with increasingx _F and reaches a value ofA _N=0.15±0.03 in the region 0.6x _F<0.8. this=" result=" provides=" new=" input=" regarding=" the=" question=" of=" the=" internal=" spin=" structure=" of=" transversely-polarized=">This work was performed at the Fermi National Accelerator Laboratory, which is operated by University Research Associates, Inc., under contract DE-AC02-76CH03000 with the U.S. Department of Energy. Work supported in part by the U.S. Department of Energy, Division of High Energy Physics, Contracts W-31-109-ENG-38, W-7405-ENG-36, DE-AC02-76ER02289, DE-AS05-76ER05096     

Comment on “the rastall model and Stapp's proof of nonlocality”

It is shown that the argument set forth as being my argument is fundamentally different from my argument.1. This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.     

Complex fragment emission from low energy compound nucleus decay to multifragmentation

In the first of these lectures, the experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and Z value are compared to the transtion state rates. In the second part, the high energy multi-fragment emission probabilities are shown to be reducible to the single fragment emission probability through the binomial distribution. The extracted one-fragment emission probabilities have a thermal dependence of the formp=e ^–B/T . This suggests that multifragmentation is a sequence of thermal binary decays.Invited lecture given at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Nuclear Physics Division of the US Department of Energy, under contract DE-AC03-76SF00098.