共查询到20条相似文献,搜索用时 15 毫秒
1.
Oussama Hijazi Sebastián Montiel Xiao Zhang 《Communications in Mathematical Physics》2001,221(2):255-265
Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues
of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized
by the existence of real Killing spinors and the minimality of the boundary.
Received: 22 August 2000 / Accepted: 15 March 2001 相似文献
2.
Under two boundary conditions, the generalized Atiyah–Patodi–Singer boundary condition and the modified generalized Atiyah–Patodi–Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary. 相似文献
3.
Ilka Agricola 《Communications in Mathematical Physics》2003,232(3):535-563
Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇
t
joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D
t
corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for
any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D
1/3. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor
with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to
the string equations and a detailed discussion of a 5-dimensional example.
Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002
RID="*"
ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft
and the Max-Planck Society. 相似文献
4.
We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the hermiticity of the Dirac operator. We then define spectral triples of noncommutative spaces with boundary. In particular we evaluate the spectral action corresponding to the noncommutative space of the standard model and show that the Einstein–Hilbert action gets modified by the addition of the extrinsic curvature terms with the right sign and coefficient necessary for consistency of the Hamiltonian. We also include effects due to the addition of a dilaton field. 相似文献
5.
In this paper, we give a new lower bound for the eigenvalues of the Dirac operator on a compact spin manifold. This estimate is motivated by the fact that in its limiting case a skew-symmetric tensor (see Eq. (1.6)) appears that can be identified geometrically with the O’Neill tensor of a Riemannian flow, carrying a transversal parallel spinor. The Heisenberg group which is a fibration over the torus is an example of this case. Sasakian manifolds are also considered to be particular examples of Riemannian flows. Finally, we characterize the 3-dimensional case by a solution of the Dirac equation. 相似文献
6.
We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue is attained. 相似文献
7.
Paolo Piazza 《Communications in Mathematical Physics》1998,193(1):105-124
Let be a closed fibration of Riemannian manifolds and let , be a family of generalized Dirac operators. Let be an embedded hypersurface fibering over B; . Let be the Dirac family induced on . Each fiber in is the union along of two manifolds with boundary . In this paper, generalizing our previous work[16], we prove general surgery rules for the local and global anomalies of the Bismut–Freed connection on the determinant bundle associated to . Our results depend heavily on the b-calculus [12], on the surgery calculus [11] and on the APS family index theory developed in [13], in particular on the notion
of spectral section for the family .
Received: 23 October 1996 / Accepted: 28 July 1997 相似文献
8.
K. -D. Kirchberg 《Journal of Geometry and Physics》2004,50(1-4):205-222
Using Weitzenböck techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator D and lower bounds for the spectrum of D2 if the curvature satisfies certain conditions. 相似文献
9.
We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator
perturbed by a scalar function. We calculate first two Gilkey–de Witt coefficients and make explicit calculations for the
case of n-spheres with a completely symmetric Dirac. In the special case of dimension 3, when such perturbation corresponds to the
completely antisymmetric torsion, we carry out the noncommutative calculation following Chamseddine and Connes (J Geom Phys
57:121, 2006) and study the case of SU
q
(2). 相似文献
10.
We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the
MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.
Mathematics Subject Classifications (2000). Differential Geometry, Global Analysis, 53C27, 53C40, 53C80, 58G25, 83C60. 相似文献
11.
Oussama Hijazi 《Communications in Mathematical Physics》1994,160(3):563-579
Kählerian twistor operators are introduced to get lower bounds for the eigenvalues of the Dirac operator on compact spin Kähler manifolds. In odd complex dimensions, manifolds with the smallest eigenvalues are characterized by an over determined system of differential equations similar to the Riemannian case. In these dimensions, we show the existence of a unique natural Kählerian twistor operator. It is also proved that, on a Kähler manifold with nonzero scalar curvature, the space of Riemannian twistor-spinors is trivial.This work has been partially supported by the EEC programme GADGET Contract Nr. SC1-0105 相似文献
12.
An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smalles possible eigenvalue is attained are also listed. Moreover, a complete classification of the compact odd-dimensional manifolds whose universal covering space is Sn−1 ×
is given in the limiting case. All such manifolds are diffeomorphic but not necessarily isometric to Sn−1 × S1. 相似文献
13.
We give an explicit construction of approximate eigenfunctions for a linearized Euler operator in dimensions two and three
with periodic boundary conditions, and an estimate from below for its spectral bound in terms of an appropriate Lyapunov exponent.
As a consequence, we prove that in dimension 2 the spectral and growth bounds for the corresponding group are equal. Therefore,
the linear hydrodynamic stability of a steady state for the Euler equations in dimension 2 is equivalent to the fact that
the spectrum of the linearized operator is pure imaginary. In dimension 3 we prove the estimate from below for the spectral
bound that implies the same equality for every example where the relevant Lyapunov exponents could be effectively computed.
For the kinematic dynamo operator describing the evolution of a magnetic field in an ideally conducting incompressible fluid
we prove that the growth bound equals the spectral bound in dimensions 2 and 3.
Received: 20 May 2002 / Accepted: 5 September 2002 Published online: 10 January 2003
RID="*"
ID="*" The first author was partially supported by the Twinning Program of the National Academy of Sciences and National Science
Foundation, and by the Research Council and Research Board of the University of Missouri.
RID="**"
ID="**" The second author was partially supported by the National Science Foundation grant DMS 9876947 and CRDF grant RM1-2084.
Acknowledgements. The authors thank Susan Friedlander for useful discussions.
Communicated by P. Constantin 相似文献
14.
K. Habermann 《Communications in Mathematical Physics》1997,184(3):629-652
Symplectic Dirac operators, acting on symplectic spinor fields introduced by B.~Kostant in geometric quantization, are canonically
defined in a similar way as the Dirac operator on Riemannian manifolds. These operators depend on a choice of a metaplectic
structure as well as on a choice of a symplectic covariant derivative on the tangent bundle of the underlying manifold. This
paper performs a complete study of these relations and shows further basic properties of the symplectic Dirac operators. Various
examples are given for illustration.
Received: 1 July 1996 / Accepted: 24 September 1996 相似文献
15.
In this paper we explain how to define “lower dimensional” volumes of any compact Riemannian manifold as the integrals of
local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any dimension. Our reasoning is motivated by an idea of Connes and involves in an essential way noncommutative geometry and the
analysis of Dirac operators on spin manifolds. However, the ultimate definitions of the lower dimensional volumes do not involve
noncommutative geometry or spin structures at all.
相似文献
16.
Yong Wang 《Letters in Mathematical Physics》2007,80(1):37-56
We prove a Kastler–Kalau–Walze type theorem for the Dirac operator and the signature operator for 3,4-dimensional manifolds
with boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action in the case
of 4-dimensional manifolds with flat boundary.
相似文献
17.
G. Grensing 《The European Physical Journal C - Particles and Fields》2002,23(2):377-387
The path integral for ghost fermions, which is heuristically made use of in the Batalin-Fradkin-Vilkovisky approach to quantization
of constrained systems, is derived from first principles. The derivation turns out to be rather different from that of physical
fermions since the definition of Dirac states for ghost fermions is subtle. With these results at hand, it is then shown that
the nonminimal extension of the Becchi-Rouet-Stora-Tyutin operator must be chosen differently from the notorious choice made
in the literature in order to avoid the boundary terms that have always plagued earlier treatments. Furthermore it is pointed
out that the elimination of states with nonzero ghost number requires the introduction of a thermodynamic potential for ghosts;
the reason is that Schwarz's Lefschetz formula for the partition function of the time-evolution operator is not capable, despite
claims to the contrary, to get rid of nonzero ghost number states on its own. Finally, we comment on the problems of global
topological nature that one faces in the attempt to obtain the solutions of the Dirac condition for physical states in a configuration
space of nontrivial geometry; such complications give rise to anomalies that do not obey the Wess-Zumino consistency conditions.
Received: 4 May 2001 / Revised version: 10 October 2001 / Published online: 8 February 2002 相似文献
18.
《Journal of Geometry and Physics》1995,17(3):283-297
General theorems on pin structures on products of manifolds and on homogeneous (pseudo-) Riemannian spaces are given and used to find explicitly all such structures on odd-dimensional real projective quadrics, which are known to be non-orientable (Cahen et al. 1993). It is shown that the product of two manifolds has a pin structure if and only if both are pin and at least one of them is orientable. This general result is illustrated by the example of the product of two real projective planes. It is shown how the Dirac operator should be modified to make it equivariant with respect to the twisted adjoint action of the Pin group. A simple formula is derived for the spectrum of the Dirac operator on the product of two pin manifolds, one of which is orientable, in terms of the eigenvalues of the Dirac operators on the factor spaces. 相似文献
19.
Daniel Maerten 《Letters in Mathematical Physics》2008,86(1):1-18
Eigenvalue estimate for the Dirac–Witten operator is given on bounded domains (with smooth boundary) of spacelike spin hypersurfaces
satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS and chiral conditions).
Roughly speaking, any eigenvalue of the Dirac–Witten operator satisfies
where is the infimum of (the opposite of) the Lorentzian norm of the constraints vector. Equality cases are also investigated and
lead to interesting geometric situations.
相似文献
20.
《Journal of Geometry and Physics》2006,56(11):2189-2202