442 research outputs found
Chiral perturbation theory for lattice QCD including O(a^2)
The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD
with Wilson fermions are constructed. The results are generalized to partially
quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory
with Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 3 pages, Lattice2003 (spectrum
On Witten's global anomaly for higher SU(2) representations
The spectral flow of the overlap operator is computed numerically along a
particular path in gauge field space. The path connects two gauge equivalent
configurations which differ by a gauge transformation in the non-trivial class
of pi_4(SU(2)). The computation is done with the SU(2) gauge field in the
fundamental, the 3/2, and the 5/2 representation. The number of eigenvalue
pairs that change places along this path is established for these three
representations and an even-odd pattern predicted by Witten is verified.Comment: 24 pages, 12 eps figure
The Dirac operator on untrapped surfaces
We establish a sharp extrinsic lower bound for the first eigenvalue of the
Dirac operator of an untrapped surface in initial data sets without apparent
horizon in terms of the norm of its mean curvature vector. The equality case
leads to rigidity results for the constraint equations with spherical boundary
as well as uniqueness results for constant mean curvature surfaces in Minkowski
space.Comment: 16 page
Generic metrics and the mass endomorphism on spin three-manifolds
Let be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page
Rigidity of compact Riemannian spin Manifolds with Boundary
In this article, we prove new rigidity results for compact Riemannian spin
manifolds with boundary whose scalar curvature is bounded from below by a
non-positive constant. In particular, we obtain generalizations of a result of
Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake
\cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et
rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
Nonexistence of Generalized Apparent Horizons in Minkowski Space
We establish a Positive Mass Theorem for initial data sets of the Einstein
equations having generalized trapped surface boundary. In particular we answer
a question posed by R. Wald concerning the existence of generalized apparent
horizons in Minkowski space
Optimal eigenvalues estimate for the Dirac operator on domains with boundary
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.Comment: 10 page
Spectral Bounds for Dirac Operators on Open Manifolds
We extend several classical eigenvalue estimates for Dirac operators on
compact manifolds to noncompact, even incomplete manifolds. This includes
Friedrich's estimate for manifolds with positive scalar curvature as well as
the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
In a recent paper, we proved that a large class of spacetimes, not
necessarily homogeneous or isotropous and relevant at a cosmological level,
possesses a preferred codimension one submanifold, i.e., the past cosmological
horizon, on which it is possible to encode the information of a scalar field
theory living in the bulk. Such bulk-to-boundary reconstruction procedure
entails the identification of a preferred quasifree algebraic state for the
bulk theory, enjoying remarkable properties concerning invariance under
isometries (if any) of the bulk and energy positivity, and reducing to
well-known vacua in standard situations. In this paper, specialising to open
FRW models, we extend previously obtained results and we prove that the
preferred state is of Hadamard form, hence the backreaction on the metric is
finite and the state can be used as a starting point for renormalisation
procedures. That state could play a distinguished role in the discussion of the
evolution of scalar fluctuations of the metric, an analysis often performed in
the development of any model describing the dynamic of an early Universe which
undergoes an inflationary phase of rapid expansion in the past.Comment: 41 page
- …