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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2009, Volume 90, Issue 11, Pages 793–799
(Mi jetpl596)
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This article is cited in 14 scientific papers (total in 15 papers)
GRAVITY, ASTROPHYSICS
$\hbar$ as parameter of Minkowski metric in effective theory
G. E. Volovikab a Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland
b Landau Institute for Theoretical Physics RAS
Abstract:
With the proper choice of the dimensionality of the metric components and matter field variables, 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 $\hbar$ 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: $g^{\mu\nu}_\mathrm{Minkowski}=\mathrm{diag}(-\hbar^2,(\hbar c)^2,(\hbar c)^2,(\hbar c)^2)$. They parametrize the equilibrium quantum vacuum state. The physical quantities which enter the covariant equations are dimensionless quantities and quantities which have dimension of rest energy $M$ or its power. Dimensionless quantities include the running coupling ‘constants’ $\alpha_i$; the geometric $\theta$-parameters which enter topological terms in action; and geometric charges coming from the group theory, such as angular momentum quantum number $j$, weak charge, electric charge $q$, hypercharge, baryonic and leptonic charges, number of atoms $N$, etc. Dimensionful parameters are mass matrices with dimension of $M$; gravitational coupling $K$ with $[K]=[M]^2$; cosmological constant with dimension $M^4$; etc. In effective theory, the interval $s$ has the dimension of $1/M$; it characterizes dynamics of particles in quantum vacuum rather than space-time geometry. The action is dimensionless reflecting equivalence between action and the phase of a wave function in quantum mechanics. We discuss the effective action, and the measured physical quantities including parameters of metrology triangle.
Received: 02.11.2009 Revised: 09.11.2009
Citation:
G. E. Volovik, “$\hbar$ as parameter of Minkowski metric in effective theory”, Pis'ma v Zh. Èksper. Teoret. Fiz., 90:11 (2009), 793–799; JETP Letters, 90:11 (2009), 697–704
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https://www.mathnet.ru/eng/jetpl596 https://www.mathnet.ru/eng/jetpl/v90/i11/p793
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Abstract page: | 246 | Full-text PDF : | 68 | References: | 30 |
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