dorsal/arxiv
View SchemaThe Einstein Action for Algebras of Matrix Valued Functions - Toy Models
| Authors | Piotr M. Hajac |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9510007 |
| URL | https://arxiv.org/abs/q-alg/9510007 |
| DOI | 10.1063/1.531662 |
Abstract
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for $M\sb 4(R)$. It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made.
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"abstract": "Two toy models are considered within the framework of noncommutative\ndifferential geometry. In the first one, the Einstein action of the Levi-Civita\nconnection is computed for the algebra of matrix valued functions on a torus.\nIt is shown that, assuming some constraints on the metric, this action splits\ninto a classical-like, a quantum-like and a mixed term. In the second model, an\nanalogue of the Palatini method of variation is applied to obtain critical\npoints of the Einstein action functional for $M\\sb 4(R)$. It is pointed out\nthat a solution to the Palatini variational problem is not necessarily a\nLevi-Civita connection. In this model, no additional assumptions regarding\nmetrics are made.",
"arxiv_id": "q-alg/9510007",
"authors": [
"Piotr M. Hajac"
],
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"q-alg",
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"doi": "10.1063/1.531662",
"title": "The Einstein Action for Algebras of Matrix Valued Functions - Toy Models",
"url": "https://arxiv.org/abs/q-alg/9510007"
},
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