منابع مشابه
Gravity from Dirac Eigenvalues
We study a formulation of euclidean general relativity in which the dynamical variables are given by a sequence of real numbers λn, representing the eigenvalues of the Dirac operator on the curved spacetime. These quantities are diffeomorphisminvariant functions of the metric and they form an infinite set of “physical observables” for general relativity. Recent work of Connes and Chamseddine su...
متن کاملFun with Dirac Eigenvalues
Amongst the lattice gauge community it has recently become quite popular to study the distributions of eigenvalues of the Dirac operator in the presence of the background gauge fields generated in simulations. There are a variety of motivations for this. First, in a classic work, Banks and Casher1 related the density of small Dirac eigenvalues to spontaneous chiral symmetry breaking. Second, la...
متن کاملGeneral Relativity in terms of Dirac Eigenvalues
The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of “observables” for general relativity. Recent work of Chamseddine and Connes suggests that they can be taken as variables for an invariant description of the gravitational field’s dynamics. We compute the Poisson brackets of these eigenvalues and find t...
متن کاملVariational Characterization for Eigenvalues of Dirac Operators
In this paper we give two diierent variational characterizations for the eigenvalues of H + V where H denotes the free Dirac operator and V is a scalar potential. The rst one is a min-max involving a Rayleigh quotient. The second one consists in minimizing an appropriate nonlinear functional. Both methods can be applied to potentials which have singularities as strong as the Coulomb potential.
متن کامل00 4 Distributions of Dirac Operator Eigenvalues
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated. As a special case, we give examples of the lowest-lying eigenvalue distributions for QCD-like gauge theories without making use of earlier re...
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ژورنال
عنوان ژورنال: Modern Physics Letters A
سال: 1998
ISSN: 0217-7323,1793-6632
DOI: 10.1142/s0217732398000541