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2009

$\hbar$ as parameter of Minkowski metric in effective theory

Volovik, G. E.

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With the proper choice of the dimensionality of the metric components, the action for all fields becomes dimensionless.

Such quantities as the vacuum speed of light c, the Planck constant \hbar, the electric charge e, the particle mass m, the Newton constant G never enter equations written in the covariant form, i.e., via the metric g^{\mu\nu}.
The speed of light c and the Planck constant are parameters of a particular two-parametric family of solutions of general relativity equations describing the flat isotropic Minkowski vacuum in effective theory emerging at low energy: g^{\mu\nu}=diag(-\hbar^2, (\hbar c)^2, (\hbar c)^2, (\hbar c)^2).
They parametrize the equilibrium quantum vacuum state.

$\hbar$ as parameter of Minkowski metric in effective theory · Around

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1995
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