Search results for " MATHEMATICAL"
showing 10 items of 686 documents
The 1-loop effective potential for the Standard Model in curved spacetime
2018
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of $\beta$-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which i…
Intersecting Defects and Supergroup Gauge Theory
2021
Journal of physics / A 54(43), 435401 (2021). doi:10.1088/1751-8121/ac2716
Algebra Structures on Hom(C,L)
1999
info:eu-repo/semantics/published
Dimensional interpolation and the Selberg integral
2019
Abstract We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non–integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.
Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy
2021
We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves. Liu, Zhang, and Zhou conjectured that the full partition function of this Dubrovin--Frobenius manifold is a tau-function of the extended nonlinear Schr\"odinger hierarchy, an extension of a particular rational reduction of the Kadomtsev--Petviashvili hierarchy. We prove a version of their conjecture specializing the Givental--M…
Deformation quantization of covariant fields
2002
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a better understanding of their quantization.
Zero rest-mass fields and the Newman-Penrose constants on flat space
2020
Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich's framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic …
Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces
2007
This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…
The use of history in mathematics education: The case of posthumous twins
2018
Se presenta un estudio exploratorio sobre un tipo particular de problemas verbales descriptivos de larga tradición e importancia en el desarrollo del pensamiento matemático: el problema de los gemelos póstumos. La metodología que sustenta el estudio tiene dos vertientes complementarias: el análisis histórico epistemológico y el análisis didáctico en los libros de texto y manuales escolares. Con énfasis en la resolución de problemas, se resalta la importancia de integrar la historia y epistemología de las ideas matemáticas en la investigación educativa, para provecho de estudiantes y profesores. An exploratory study is presented on a particular type of descriptive word problems of long tradi…
Ģeometrijas jautājumi
1932
Izdevumam nav titullapas. Lekciju nosaukuma varianti un gads norādīti sējuma sākumā, ierakstīti ar zīmuli.