A Hamiltonian formulation of causal variational principles
نویسندگان
چکیده
منابع مشابه
Causal variational principles on measure spaces
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied t...
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A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are suppleme...
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The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a diffeomorphism. Then the constructions are extended to convex combinations of such measures, leading to perturbation expansions for the mean and the fluctuatio...
متن کاملJa n 20 09 CAUSAL VARIATIONAL PRINCIPLES ON MEASURE SPACES
Causal variational principles on measure spaces are introduced. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied to variational principles formulated in indefinite inner product spaces.
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2017
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-017-1153-5