The gravity of the classical field of quantum mechanics (original) (raw)
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The Spinor-Tensor Gravity of the Classical Dirac Field
Symmetry
In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, has been generalized to the curved space-time in the covariant form. Thence, the metric of space-time has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the “cosmological” gravity tensor (CGT), a generalization of the classical cosmological constant (CC), as a part of the energy-impulse tensor density (EITD). Even if the classical cosmological constant is set to zero, the CGT is non-zero, allowing a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical macroscopic limit, the general relativity equation is recovered. In the perturbative approach, the CGT leads to a second-...
The quantum hydrodynamic representation in curved space and the related Einstein equation
2017
The work shows that the evolution of quantum states in the hydrodynamic representation can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of a cosmological energy impulse tensor density (CEITD) that in the classical limit converges to a constant. The mean value of CEITD in the galactic space leads to the correct order of magnitude of the cosmological constant. The coupling of the quantum gravitational equation with half-spin fermions is finally developed.
2017
In this work the scalar free Klein-Gordon field coupled to the quantum mechanical gravity equation (QMGE), that takes into account the quantum property of matter, is quantized. The model has been developed at the first order in the metric tensor with a self-consistent analytical dependence of the energy impulse tensor by the quantum field. The quantum behavior, due to the quantum potential energy, in the gravity equation (GE) has been investigated by studying the energy-impulse tensor density generated the quantum field. The outputs of the theory show that the vacuum energy density of the zero point is effective for the cosmological constant only in the volume of space where the mass is localized in particles or in high gravity bodies, leading to a cosmological effect on the motion of the galaxies that is compatible with the astronomical observations. The paper shows that the energy-impulse tensor density makes the QMGE, in the quasi-Euclidean limit, physically independent by the le...
The Hydrodynamic Gravity of the Classical Klein-Gordon field
arXiv (Cornell University), 2017
The work shows that the evolution of the field of the free Klein-Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been covariantly extended to the curved space-time, the gravity equation (GE), determining the geometry of the space-time, is obtained by minimizing the overall action comprehending the gravitational field. The derived Einstein-like gravity for the KGE field shows an energy-impulse tensor density (EITD) that is a function of the field with the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant(CC). The energy-impulse tensor of the theory shows analogies with the modified Brans-Dick gravity with an effective gravity constant G divided by the field squared. Even if the classical cosmological constant is set to zero, the model shows the emergence of a theory-derived quantum CPTD that, in principle, allows to have a stable quantum vacuum (out of the collapsed branched polymer phase) without postulating a non-zero classical CC. In the classical macroscopic limit, the gravity equation of the KGE field leads to the Einstein equation. Moreover, if the boson field of the photon is considered, the EITD correctly leads to its electromagnetic energy-impulse tensor density. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it tends to zero as the space-time approaches to the flat vacuum, leading to an overall cosmological effect on the motion of the galaxies that may possibly be compatible with the astronomical observations.
Galaxies, 2016
In the present work, it is shown that the problem of the cosmological constant (CC) is practically the consequence of the inadequacy of general relativity to take into account the quantum property of the space. The equations show that the cosmological constant naturally emerges in the hydrodynamic formulation of quantum gravity and that it does not appear in the classical limit because the quantum energy-impulse tensor gives an equal contribution with opposite sign. The work shows that a very large local value of the CC comes from the space where the mass of a quasi-punctual particle is present but that it can be as small as measured on cosmological scale. The theory shows that the small dependence of the CC from the mean mass density of the universe is due to the null contribution coming from the empty space. This fact gives some hints for the explanation of the conundrum of the cosmic coincidence by making a high CC value of the initial instant of universe compatible with the very small one of the present era.
Symmetry
Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend general...
On the correspondence between classical and quantum gravity
Classical and Quantum Gravity, 2001
The relationship between the classical and quantum theories of gravity is reexamined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that the potential so defined fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of theh 0-order part of the loop corrections is given directly in terms of the effective action. Gauge independence of that part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed.
arXiv (Cornell University), 2017
The work shows that the evolution of the field of the free Klein-Gordon equation, in the hydrodynamic representation, can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of the cosmological energy impulse tensor density (CEITD) in the gravity equation. The scalar free Klein-Gordon field coupled to the gravity equation (GE), with the analytical dependence of the energy impulse tensor as a function of the field, is quantized at the first order in the metric tensor. The cosmological constant (CC), generated the quantum field, has been investigated and calculated for the vacuum. The outputs of the theory show that the vacuum energy density of the zero point is effective for the cosmological constant only in the volume of space where the mass is localized in particles or in high gravity bodies, leading to a cosmological effect on the motion of the galaxies that is compatible with the astronomical observations. The paper shows that, in the quasi-Euclidean limit, the energy-impulse tensor density makes the GE asymptotically independent by the zero-point energy density of the vacuum, and possibly compatible with the renormalization techniques of the QFT.
An introduction to quantum gravity
2011
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental interactions, while giving rise to new developments in mathematics. The various competing theories, e.g. string theory and loop quantum gravity, have still to be checked against observations. We review the classical and quantum foundations necessary to study field-theory approaches to quantum gravity, the passage from old to new unification in quantum field theory, canonical quantum gravity, the use of functional integrals, the properties of gravitational instantons, the use of spectral zeta-functions in the quantum theory of the universe, Hawking radiation, some theoretical achievements and some key experimental issues.