General reference frames and their associated space manifolds
Mayeul Arminjon,Frank Reifler +1 more
TLDR
In this article, a formal definition of a general reference frame in general spacetime, as an equivalence class of charts, was proposed, which corresponds with the notion of a reference frame as being a (fictitious) deformable body.Abstract:
We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we assume, moreover, that the time coordinate is fixed. This is necessary for quantum mechanics, because the Hamiltonian operator depends on the choice of the time coordinate. Our definition allows us to associate rigorously with each reference frame F, a unique "space" (a three-dimensional differentiable manifold), which is the set of the world lines bound to F. This also is very useful for quantum mechanics. We briefly discuss the application of these concepts to Godel's universe.read more
Citations
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Basic quantum mechanics for three Dirac equations in a curved spacetime
Mayeul Arminjon,Frank Reifler +1 more
TL;DR: In this article, the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime was studied by extending Pauli's method, and it was shown that the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product.
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A non-uniqueness problem of the Dirac theory in a curved spacetime
Mayeul Arminjon,Frank Reifler +1 more
TL;DR: In this article, the authors studied the conditions under which a change of the Dirac matrices leads to an equivalent Hamiltonian operator H or an equivalent energy operator E in a curved spacetime.
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Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations
Mayeul Arminjon,Frank Reifler +1 more
TL;DR: In this paper, it was shown that the generalized de Broglie relations in a curved space-time are a direct consequence of Whitham's Lagrangian method and not just a physical hypothesis as introduced by Einstein and debroglie and by many quantum mechanics textbooks.
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Canonical frame-indifferent transport operators with the four-dimensional formalism of differential geometry☆
TL;DR: In this article, the Truesdell transport is shown to be the only transport that is invariant with respect to superposed rigid body motions in a constitutive model of the Cauchy tensor.
Journal ArticleDOI
Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
Mayeul Arminjon,Frank Reifler +1 more
TL;DR: In this paper, it was shown that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and debroglie, and by many quantum mechanics textbooks.
References
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An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation
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General-relativistic celestial mechanics. I. Method and definition of reference systems.
TL;DR: A new formalism for treating the general-relativistic celestial mechanics of systems of system of arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies is presented, aimed at yielding a complete description of the global dynamics of such $N-body systems.
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General relativity: Relative standard mass, momentum, energy and gravitational field in a general system of reference
TL;DR: In this article, it was shown that the equations of the motion of a free test particle in General Relativity, with respect to any physical system of reference, can always have the classical interpretation: time derivative of momentum =mass ×gravitational field.