The bicomplex quantum Coulomb potential problem

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi is a bicomplex number. Following Pauli's algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrodinger's time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J. Phy

Operator Coproduct-Realization of Quantum Group Transformations in Two Dimensional Gravity, I.

A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for spins \demi and $J$) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of $U_q(sl(2))$ realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended $U_q(sl(2))$ algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the screening charges of 2D gravity.Comment: 33 pages, latex, no figure

A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations

We consider the universal solution of the Gervais-Neveu-Felder equation in the ${\cal U}_q(sl_2)$ case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to quantum 3-j and 6-j symbols. Finally, we use this solution to build a q-deformation of the trigonometric Lam\'e equation.Comment: 9 pages, 4 figure

Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199

Why has home ownership fallen among the young?

We document that home ownership of households with 'heads' aged 25-44 years fell substantially between 1980 and 2000 and recovered only partially during the 2001-2005 housing boom. The 1980-2000 decline in young home ownership occurred as improvements in mortgage opportunities made it easier to purchase a home. This paper uses an equilibrium life-cycle model calibrated to micro and macro evidence to understand why young home ownership fell over a period when it became easier to own a home. Our findings indicate that a trend toward marrying later and the increase in household earnings risk that occurred after 1980 account for 3/5 to 4/5 of the decline in young home ownership.Housing, home ownership, tenure choice, first-time home-buyers, marriage, income risk

Why has home ownership fallen among the young?

We document that home ownership of households with "heads" aged 25 - 44 years fell substantially between 1980 and 2000 and recovered only partially during the 2001-2005 housing boom. The 1980-2000 decline in young home ownership occurred as improvements in mortgage opportunities made it easier to purchase a home. This paper uses an equilibrium life-cycle model calibrated to micro and macro evidence to understand why young home ownership fell over a period when it became easier to own a home. Our findings indicate that a trend toward marrying later and the increase in household earnings risk that occurred after 1980 account for 3/5 to 4/5 of the decline in young home ownership.Home ownership ; Marriage

Reactor power systems for manned earth orbital applications

Design requirements for reactor power system of manned earth orbital space statio

First-time home buyers and residential investment volatility

Like other macroeconomic variables, residential investment has become much less volatile since the mid-1980s (recent experience notwithstanding.) This paper explores the role of structural change in this decline. Since the early 1980s there have been many changes in the underlying structure of the economy, including those in the mortgage market which have made it easier to acquire a home. We examine how these changes affect residential investment volatility in a life-cycle model consistent with micro evidence on housing choices. We find that a decline in the rate of household formation, increased delay in marriage, and an increase in the cross-sectional variance of earnings drive the decline in volatility. Our findings provide support for the view that the “Great Moderation” in aggregate fluctuations is not just due to smaller aggregate shocks, but is driven at least in part by structural change.Home ownership ; Mortgages

Drell-Hearn-Gerasimov Sum Rule for the Nucleon in the Large-N_c Limit

We show that the Drell-Hearn-Gerasimov sum rule for the nucleon is entirely saturated by the \Delta resonance in the limit of a large number of colors, N_c \to \infty. Corrections are at relative order 1/N_c^2.Comment: 6 pages, latex, no figure