共查询到20条相似文献,搜索用时 31 毫秒
1.
A. A. Andrianov V. A. Andrianov P. Giacconi R. Rodenberg R. Soldati 《Journal of Mathematical Sciences》2008,151(2):2801-2812
The mechanism of generation of the Standard Model for fermions on the domain wall in five-dimensional space-time is presented.
As a result of self-interaction of five-dimensional fermions and gravity induced by matter fields, in the strong coupling
regime, in the model there arises a spontaneous translational symmetry breaking, which leads to localization of light particles
on a 3 + 1-dimensional domain wall (“3-brane”) that is embedded into a five-dimensional anti-de Sitter space-time (AdS5). Appropriate low-energy, effective action, classical kink-like vacuum configurations for the gravity and scalar fields are
investigated. Mass spectra for light composite particles and their coupling constants interaction in ultra-low-energy, which
localize on the brane, are explored. We establish estimates of characteristic scales and constants interactions of the model
and also a relation between the bulk five-dimensional gravitational constant, curvature of AdS5 space-time, and brane Newton’s constants. The induced cosmological constant on the brane exactly vanishes in all orders of
the theory perturbation. We find out that scalar interaction is strongly suppressed at ultra-low-energy, and the brane fluctuations
(branons) are suitable “sterile” canditates for explanation of the phenomenon of Dark Matter. Bibliography: 21 titles.
Dedicated to the 100th birthday of M. P. Bronstein
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 5–29. 相似文献
2.
K. B. Alkalaev 《Theoretical and Mathematical Physics》2006,149(1):1338-1348
Using the su(2, 2) spinor language, we describe free mixed-symmetry massless bosonic and fermionic gauge fields of arbitrary
spins in the AdS5 space. We construct manifestly covariant action functionals and derive field equations.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 47–59, October, 2006. 相似文献
3.
We study conserved currents of any integer or half-integer spin built from massless scalar and spinor fields inAdS
3. We show that 2-forms dual to the conserved currents inAdS
3 are exact in the class of infinite expansions in higher derivatives of the matter fields with the coefficients containing
inverse powers of the cosmological constant. This property has no analogue in the flat space and may be related to the holography
of the AdS spaces. “Improvements” to the physical currents are described as the trivial local current cohomology class. A
complex (TS, D) of spin-s currents is defined, and the cohomology group H1(TS, D)= ℂ2s+1is found.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 3–25, April, 2000. 相似文献
4.
Paolo Camassa 《Annales Henri Poincare》2007,8(8):1433-1459
We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset
of the space-time and is not irreducible: the commutant and the causal complement have to be considered relatively to the
ambient space. We prove this relative form of Haag duality under quite general conditions for the free scalar and electromagnetic
field of space dimension d ≥ 2 in the vacuum representation. Such property is interesting in view of a theory of superselection sectors for the electromagnetic
field.
Supported by the EU network “Quantum Spaces – Noncommutative Geometry” HPRN-CT-2002-00280.
Submitted: August 1, 2006. Accepted: March 2, 2007. 相似文献
5.
We consider a particular class of AdS
d
mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux. We find unique gauge-invariant free actions and analyze the equations of motion. 相似文献
6.
A. T. Filippov 《Theoretical and Mathematical Physics》2010,163(3):753-767
We propose new models of the “affine” theory of gravity in multidimensional space-times with symmetric connections. We use
and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposed method for obtaining the geometry using
the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric” Lagrangian that
is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, other fundamental tensors)
expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard
Einstein theory with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic)
meson, and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation.
The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice
of the Lagrangian determines further details of the theory, for example, the nature of the fields that can describe massive
particles, tachyons, or even “phantoms.” In “natural” geometric theories, dark energy must also arise. The basic parameters
of the theory (cosmological constant, mass, possible dimensionless constants) are theoretically indeterminate, but in the
framework of modern “multiverse” ideas, this is more a virtue than a defect. We consider further extensions of the affine
models and in more detail discuss approximate effective (“physical”) Lagrangians that can be applied to the cosmology of the
early Universe. 相似文献
7.
D. V. Bykov 《Proceedings of the Steklov Institute of Mathematics》2011,272(1):47-57
We consider the AdS4 × ℂℙ3 IIA superstring sigma model in the background of a “spinning string” classical solution with two charges. In the limit when
one of the spins is infinite, there are massless excitations which govern the long-range worldsheet properties of the model.
We obtain a sigma model of ℂℙ3 with fermions which describes the dynamics of these massless modes. 相似文献
8.
E. D. Livshits 《Proceedings of the Steklov Institute of Mathematics》2011,272(1):107-118
We discuss new models of an “affine” theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposal to specify the space-time
geometry by the use of the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric”
Lagrangian that is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, of other
fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements
the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive
(or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation.
The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice
of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields
that can describe massive particles, tachyons, or even “phantoms.” In “natural” geometric theories, which are discussed here,
dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly
considering approximate cosmological models inspired by the geometric approach. 相似文献
9.
Lorenzo Mazzieri 《manuscripta mathematica》2009,129(2):137-168
In this paper we construct constant scalar curvature metrics on the generalized connected sum
M = M1 \sharpK M2{M = M_1 \, \sharp_K \, M_2} of two compact Riemannian scalar flat manifolds (M
1, g
1) and (M
2, g
2) along a common Riemannian submanifold (K, g
K
) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero)
constant scalar curvature metrics on the generalized connected sum of M
1 and M
2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero
constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the (1+) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat
metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact
time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction. 相似文献
10.
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau
structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional
symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics
and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M. 相似文献
11.
Ilya A. Krishtal Benjamin D. Robinson Guido L. Weiss Edward N. Wilson 《Journal of Geometric Analysis》2007,17(1):87-96
An orthonormal wavelet system in ℝd, d ∈ ℕ, is a countable collection of functions {ψ
j,k
ℓ
}, j ∈ ℤ, k ∈ ℤd, ℓ = 1,..., L, of the form
that is an orthonormal basis for L2 (ℝd), where a ∈ GLd (ℝ) is an expanding matrix. The first such system to be discovered (almost 100 years ago) is the Haar system for which L
= d = 1, ψ1(x) = ψ(x) = κ[0,1/2)(x) − κ[l/2,1)
(x), a = 2. It is a natural problem to extend these systems to higher dimensions. A simple solution is found by taking appropriate
products Φ(x1, x2, ..., xd) = φ1 (x1)φ2(x2) ... φd(xd) of functions of one variable. The obtained wavelet system is not always convenient for applications. It is desirable to
find “nonseparable” examples. One encounters certain difficulties, however, when one tries to construct such MRA wavelet systems.
For example, if a = (
1-1
1 1
) is the quincunx dilation matrix, it is well-known (see, e.g., [5]) that one can construct nonseparable Haar-type scaling
functions which are characteristic functions of rather complicated fractal-like compact sets. In this work we shall construct
considerably simpler Haar-type wavelets if we use the ideas arising from “composite dilation” wavelets. These were developed
in [7] and involve dilations by matrices that are products of the form ajb, j ∈ ℤ, where a ∈ GLd(ℝ) has some “expanding” property and b belongs to a group of matrices in GLd(ℝ) having |det b| = 1. 相似文献
12.
Sourav Chatterjee Ron Peled Yuval Peres Dan Romik 《Geometric And Functional Analysis》2010,20(4):870-917
Given a Poisson point process of unit masses (“stars”) in dimension d ≥ 3, Newtonian gravity partitions space into domains of attraction (cells) of equal volume. In earlier work, we showed the
diameters of these cells have exponential tails. Here we analyze the quantitative geometry of the cells and show that their
large deviations occur at the stretched-exponential scale. More precisely, the probability that mass exp(−R
γ
) in a cell travels distance R decays like exp(-Rfd(g)){\left(-R^{f_d(\gamma)}\right)} where we identify the functions f
d
(·) exactly. These functions are piecewise smooth and the discontinuities of f¢d{f^{\prime}_d} represent phase transitions. In dimension d = 3, the large deviation is due to a “distant attracting galaxy” but a phase transition occurs when f
3(γ) = 1 (at that point, the fluctuations due to individual stars dominate). When d ≥ 5, the large deviation is due to a thin tube (a “wormhole”) along which the star density increases monotonically, until
the point f
d
(γ) = 1 (where again fluctuations due to individual stars dominate). In dimension 4 we find a double phase transition, where
the transition between low-dimensional behavior (attracting galaxy) and highdimensional behavior (wormhole) occurs at γ = 4/3. 相似文献
13.
In this article, we generalize known integral formulae (due to Brito–Langevin–Rosenberg, Ranjan and the second author) for
foliations of codimension 1 or unit vector fields and obtain an infinite series of such formulae involving invariants of the
Weingarten operator of a unit vector field, of the Jacobi operator in its direction, and their products. We write several
such formulae explicitly, on locally symmetric spaces as well as on arbitrary Riemannian manifolds where they involve also
covariant derivatives of the Jacobi operator. We work also with foliations of codimension 1 (or vector fields) which admit
“good” (in a sense) singularities. 相似文献
14.
The model of a domain wall (“thick brane”) in a noncompact five-dimensional space-time with asymmetric geometries of AdS type
aside the brane is proposed. This model is generated by fermion self-interaction in the presence of gravity. Asymmetric geometries
in the bulk are provided by a space defect in the scalar field potential and the related defect of cosmological constant.
The possibility of localization of scalar modes on such “thick branes” is studied. Bibliography: 21 titles. 相似文献
15.
The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra
and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A
! to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers
in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary “period” and piecewise-Koszul
algebras with arbitrary “jump-degree”. 相似文献
16.
The idea of a finite collection of closed sets having “linearly regular intersection” at a point is crucial in variational
analysis. This central theoretical condition also has striking algorithmic consequences: in the case of two sets, one of which
satisfies a further regularity condition (convexity or smoothness, for example), we prove that von Neumann’s method of “alternating
projections” converges locally to a point in the intersection, at a linear rate associated with a modulus of regularity. As
a consequence, in the case of several arbitrary closed sets having linearly regular intersection at some point, the method
of “averaged projections” converges locally at a linear rate to a point in the intersection. Inexact versions of both algorithms
also converge linearly.
Research of A.S. Lewis supported in part by National Science Foundation Grant DMS-0504032.
Research of D.R. Luke supported in part by National Science Foundation Grant DMS-0712796. 相似文献
17.
Károly Bezdek 《Discrete and Computational Geometry》2012,47(2):275-287
A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a “fat” one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm’s theorem
and its proof on illuminating convex bodies of constant width to the family of “fat” spindle convex bodies. Also, this leads
to the spherical analog of the well-known Blaschke–Lebesgue problem. 相似文献
18.
B. I. Sokil 《Ukrainian Mathematical Journal》1997,49(6):976-983
For a nonlinear Klein-Gordon equation, we construct the first approximation of an asymptotic solution by using Ateb-functions.
The resonance and nonresonance cases are considered.
“L’vivs’ka Politeknika” University, Lviv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 872–877,
June, 1997. 相似文献
19.
Andrzej Herdegen 《Annales Henri Poincare》2006,7(2):253-301
Casimir effect in most general terms may be understood as a backreaction of a quantum system causing an adiabatic change of
the external conditions under which it is placed. This paper is the second installment of a work scrutinizing this effect
with the use of algebraic methods in quantum theory. The general scheme worked out in the first part is applied here to the
discussion of particular models. We consider models of the quantum scalar field subject to external interaction with “softened”
Dirichlet or Neumann boundary conditions on two parallel planes. We show that the case of electromagnetic field with softened
perfect conductor conditions on the planes may be reduced to the other two. The “softening” is implemented on the level of
the dynamics, and is not imposed ad hoc, as is usual in most treatments, on the level of observables. We calculate formulas for the backreaction energy in these
models. We find that the common belief that for electromagnetic field the backreaction force tends to the strict Casimir formula
in the limit of “removed cutoff” is not confirmed by our strict analysis. The formula is model dependent and the Casimir value
is merely a term in the asymptotic expansion of the formula in inverse powers of the distance of the planes. Typical behaviour
of the energy for large separation of the plates in the class of models considered is a quadratic fall-of. Depending on the
details of the “softening” of the boundary conditions the backreaction force may become repulsive for large separations.
Communicated by Klaus Fredenhagen
submitted 9/09/04, accepted 1/07/05 相似文献
20.
We prove a generalization of the Krasnosel’ski theorem on star-shaped sets. Usingd-segments inn-dimensional Minkowski spaces instead of usual segments, the notions “d-visibility” and “d-star-shapedness” are introduced. Our main aim is to give necessary and sufficient conditions ford-star-shapedness in finite-dimensional normed spaces. 相似文献