Noncommutative Geometry and Gauge Theory on Fuzzy Sphere

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left $U(N+1)$ transformation of the field, where a field is a bimodule over the quantized algebra \CA_N. The interaction with a complex scalar field is also given.Comment: LaTeX 26 pages, final version (Dec.1999) accepted in CMP. An extra term in the gauge action is discusse

Fractional quantum Hall effect on the two-sphere: a matrix model proposal

We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two-sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states and filling fraction and show the compatibility of our result with the Haldane spherical wavefunctions.Comment: 26 pages, LaTeX, no figures, references adde

Differential Calculus on Fuzzy Sphere and Scalar Field

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.Comment: LaTeX 12 page

On the Quantum Lorentz Group

The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance between the SL(2,C) and Lorentz quantum groups.Comment: 17 page

Winners and Losers from Enacting the Financial Modernization Statute

Previous studies of the announcement effects of relaxing administrative and legislative restraints show that signal events leading up to the enactment of the Financial Services Modernization Act (FSMA) increased the prices of several classes of financial-institution stocks. An unsettled question is whether the gains observed for these stocks arise mainly from projected increases in efficiency or from reductions in customer or competitor bargaining power. This paper documents that the value increase came at the expense of customers and competitors. The stock prices of credit-constrained customers declined during FSMA event windows and experienced significant increases in beta in the wake of its enactment. These findings reinforce evidence in the literature on bank mergers that large-bank consolidation is adversely affecting access to credit for capital-constrained firms.

Monopole Bundles over Fuzzy Complex Projective Spaces

We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N -> infinity limit, where N labels the representation of the fuzzy algebra.Comment: 30 pages, LaTeX, published version; extended discussion on asymptotic Chern number

Event-Study Evidence of the Value of Relaxing Longstanding Regulatory Restraints on Banks, 1970-2000

In a partial-equilibrium model, removing a binding constraint creates value. However, in general equilibrium, the stakes of other parties in maintaining the constraint must be examined. In financial deregulation, the fear is that expanding the scope and geographic reach of very large institutions might unblock opportunities to build market power from informational advantages and size-related safety-net subsidies. This paper reviews and extends event-study evidence about the distribution of the benefits and costs of relaxing longstanding geographic and product-line restrictions on U.S. financial institutions. The evidence indicates that the new financial freedoms may have redistributed rather than created value. Event returns are positive for some sectors of the financial industry and negative for others. Perhaps surprisingly, where customer event returns have been investigated, they prove negative.

Non-commutative Euclidean structures in compact spaces

Based on results for real deformation parameter q we introduce a compact non- commutative structure covariant under the quantum group SOq(3) for q being a root of unity. To match the algebra of the q-deformed operators with necesarry conjugation properties it is helpful to define a module over the algebra genera- ted by the powers of q. In a representation where X is diagonal we show how P can be calculated. To manifest some typical properties an example of a one-di- mensional q-deformed Heisenberg algebra is also considered and compared with non-compact case.Comment: Changed conten

Quantum Group Gauge Theories and Covariant Quantum Algebras

The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields transformed as comodules under the coaction of the gauge quantum group $G_{q}$. Using this approach we construct the quantum deformations of the topological Chern-Simons models, non-abelian gauge theories and the Einstein gravity. The noncommutative fields in these models generate $G_{q}$-covariant quantum algebras.Comment: 12 pages, LaTeX, JINR preprint E2-93-54, Dubna (19 February 1993