118 research outputs found
Super self-duality for Yang-Mills fields in dimensions greater than four
Self-duality equations for Yang-Mills fields in d-dimensional Euclidean
spaces consist of linear algebraic relations amongst the components of the
curvature tensor which imply the Yang-Mills equations. For the extension to
superspace gauge fields, the super self-duality equations are investigated,
namely, systems of linear algebraic relations on the components of the
supercurvature, which imply the self-duality equations on the even part of
superspace. A group theory based algorithm for finding such systems is
developed. Representative examples in various dimensions are provided,
including the Spin(7) and G(2) invariant systems in d=8 and 7, respectively.Comment: 51 pages, late
The hidden symmetry algebras of a class of quasi-exactly solvable multi dimensional operators
Let denote the vector space of polynomials of maximal degree less
than or equal to in independent variables. This space is preserved by
the enveloping algebra generated by a set of linear, differential operators
representing the Lie algebra . We establish the counterpart of this
property for the vector space for any values of the
integers . We show that the operators preserving
generate an abstract superalgebra (non linear if ).
A family of algebras is also constructed, extending this particular algebra by
arbitrary complex parameters.Comment: 19 pages, late
Term Structure of Interest Rates.Emergence of Power Laws and Scaling Laws
The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ``microscopic'' level.interest rates, scaling laws
Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws
The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ''microscopic'' level.Interest rates scaling laws
Special Graphs
A special p-form is a p-form which, in some orthonormal basis {e_\mu}, has
components \phi_{\mu_1...\mu_p} = \phi(e_{\mu_1},..., e_{\mu_p}) taking values
in {-1,0,1}. We discuss graphs which characterise such forms.Comment: 8 pages, V2: a texing error correcte
Warped Kaluza-Klein Towers Revisited
Inspired by the warped Randall Sundrum scenario proposed to solve the mass
scale hierarchy problem with a compactified fifth extra dimension, a similar
model with no metric singularities has been elaborated. In this framework, the
Kaluza-Klein reduction equations for a real massless scalar field propagating
in the bulk have been studied carefully from the point of view of hermiticity
so as to formulate in a mathematically rigorous way all the possible boundary
conditions and corresponding mass eigenvalue towers and tachyon states. The
physical masses as observable in our four-dimensional brane are deduced from
these mass eigenvalues depending on the location of the brane on the extra
dimension axis. Examples of mass towers and tachyons and related field
probability densities are presented from numerical computations performed for
some arbitrary choices of the parameters of the model.Comment: 34 pages, 5 figure
Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws
The technique of Pad\'e Approximants, introduced in a previous work, is
applied to extended recent data on the distribution of variations of interest
rates compiled by the Federal Reserve System in the US. It is shown that new
power laws and new scaling laws emerge for any maturity not only as a function
of the Lag but also as a function of the average inital rate. This is
especially true for the one year maturity where critical forms and critical
exponents are obtained. This suggests future work in the direction of
constructing a theory of variations of interest rates at a more ``microscopic''
level.}Comment: 22 pages, 9 figures and 2 table
Study of Quommutators of Quantum Variables and Generalized Derivatives
A general deformation of the Heisenberg algebra is introduced with two
deformed operators instead of just one. This is generalised to many variables,
and permits the simultaneous existence of coherent states, and the
transposition of creation operators.Comment: 17 pages (Previous version was truncated in transmission
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