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Bohmian Quantum Gravity and Cosmology
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Nelson Pinto-Neto, Ward Struyve
However, there is an immediate problem with this ansatz, namely that Eq. (10.122) is not consistent. The Einstein tensor Gµv is identically conserved, i.e., ∇µGµv ≡ 0. So the Bohmian energy-momentum tensor Tµv(φB, g) must be conserved as well. However, the equation of motion for the scalar field does not guarantee this. (Similarly, in the Bohmian approach to nonrelativistic systems, the energy is generically not conserved.) The solution to the problem is that the usual expression for the Bohmian energy-momentum tensor is not the right source term in the Einstein field equations. The correct source term can in principle be derived by starting from the Bohmian Wheeler–DeWitt theory. However, in the derivation the gauge invariance, which in this case is the invariance under spatial diffeomorphisms (i.e., spatial coordinate transformations), should be dealt with, either by performing a gauge fixing or by working with gauge independent degrees of freedom. However, this is a notoriously difficult problem in the case of general relativity. In the case of minisuperspace model the spacial diffeomorphism invariance is eliminated and a consistent semiclassical approximation can be found straightforwardly.
QED treatment of linear elastic waves in asymmetric environments
Published in Waves in Random and Complex Media, 2021
Maysam Yousefian, Mehrdad Farhoudi
In this way, we assume the microstructures of a medium being as four-dimensional linear rigid rotors with four-dimensional angular rotation , which 's (as vibration and relative velocity of parts of each microstructure) are related to 's (as rotation in fourth dimension) via the Wick rotation. On the other hand, by selecting an appropriate gauge, we choose a gauge fixing in such a way that the displacement and rotation wave equations of motion to be covariant, and in general, the corresponding velocities of waves, masses and coupling (to the displacement field) of being different from those of . In this respect, we assume the gauge with metric for check-letters, where is the speed of wave for waves of vibration. Then, we plausibly generalize Equation (7) as with metric for tilde-letters, where is the speed of wave for waves of rotation. In Equation (14), the part using gauge (13), is just Equation (7), and the extra part again due to gauge (13), is the wave equation of vibration , i.e.
Reduction of the classical electromagnetism to a two-dimensional curved surface
Published in Journal of Modern Optics, 2019
The first theory is then described by the ordinary vector potential with components , out of which only one is independent after gauge fixing and exploiting the Gauss law, and the second one by a single scalar field , with no gauge freedom and no Gauss law. In this latter case, the Lagrangian of the free electromagnetism would have the form usual for the scalar field: