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Is minimal coupling procedure compatible with minimal action principle?

Alberto Saa
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Abstract

When space-time is assumed to be non-Riemannian the minimal coupling procedure (MCP) is not compatible, in general, with minimal action principle (MAP). This means that the equations gotten by applying MCP to the Euler-Lagrange equations of a Lagrangian $\cal L$ do not coincide with the Euler-Lagrange equations of the Lagrangian obtained by applying MCP to $\cal L$. Such compatibility can be restored if the space-time admits a connection-compatible volume element. We show how these concepts can alter qualitatively the predictions of the Einstein-Cartan theory of gravity.

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Alberto Saa. 1994-05-24. Is minimal coupling procedure compatible with minimal action principle?. https://arxiv.org/abs/gr-qc/9405054

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