Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory (original) (raw)
Related papers
Outline of a generally covariant quantum field theory and a quantum theory of gravity
We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the theory. We present the explicit calculation of the transition probability between two volume eigenstates as an example. We discuss the choices on which the T-theory relies, and the possibilities of modifying them.
Hamiltonian approach to GR - Part 2: covariant theory of quantum gravity
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly-covariant Hamilton equations and the related Hamilton-Jacobi theory. As shown here the connection with CQG-theory is achieved via the classical GR Hamilton-Jacobi equation, leading to the realization of the CQG-wave equation in 4-scalar form for the corresponding CQG-state and wave-function. The new quantum wave equation exhibits well-known formal properties characteristic of quantum mechanics, including the validity of quantum hydrodynamic equations and suitably-generalized Heisenberg inequalities. In addition, it recovers the classical GR equations in the semiclassical limit, while admitting the possibility of developing further perturbative approximation schemes. Applications of the theory are pointed out with particular reference to the construction of the stationary vacuum CQG-wave equation. The existence of a corresponding discrete energy spectrum is pointed out, which provides a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. PACS numbers: 02.30.Xx, 04.20.Cv, 04.20.Fy, 04.60.Bc, 04.60.Ds, 04.60.Gw, 11.10.Ef
The Quantum Gravity Lagrangian
2013
- makes some calculations from a quantum gravity theory and sketches a framework for further predictions. This paper defends in detail the lagrangian for quantum gravity, based on the theory in our earlier paper, by examining the simple physical dynamics behind general relativity and gauge theory. General relativity predictions from Newtonian gravity lagrangian, with a relativistic metric In 1915, Einstein and Hilbert derived the field equation of general relativity from a very simple lagrangian. The classical "proper path" of a particle in a gravitational field is the minimization of action: S = ∫ Ldt = ∫ Ld 4 x = ∫R(-g) 1/2 c 4 /(16πG)d 4 x where the Lagrangian energy L = E kinetic-E potential , and energy density is L = L/volume), which gives Einstein's field equation of general relativity when action is minimized, i.e. when dS = 0, found by "varying" the action S using the Euler-Lagrange law. To Weyl and his followers today, the "Holy Grail" of quantum gravity research remains the task of obtaining a theory which at low energy has the Lagrangian gravitational field energy density component, L = R(-g) 1/2 c 4 /(16πG), so that it yields produces Einstein's field equation as a "weak field" limit or approximation.
The gravity of the classical field of quantum mechanics
2020
In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated to the Dirac field is derived. The hydrodynamic representation of the Dirac equation have been generalizaed to the curved space-time in the covariant form. Thence, the metric of the spacetime has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the cosmological gravity tensor (CGT) as a part of the energy-impulse tensor density (EITD) that in the classical limit leads to the cosmological constant (CC). Even if the classical cosmological constant is set to zero, the CGT is non zero, allowing to have a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical limit, the gravity equation leads to the general relativity equation. In the perturbative approach, the CGT leads to a second order correction to the Newtonian gravity that takes contribution from the space where the ...
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...
From general relativity to quantum gravity
Lecture Notes in Physics, 1982
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades. 1
1992
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter stage of cosmological evolution at an arbitrary value of Λ-a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scalar mode and the short distance general relativistic limit in a special frame which is related by a nonlocal conformal transformation to the original metric. The role of compactness and regularity of spacetime in the Euclidean version of the Schwinger-Keldysh technique is discussed.
Quantum Field Theory in Gravitational Background
NATO ASI Series, 1986
We discuss quantum fields on Riemannian space-time. A principle of local definiteness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows us to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non-stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non-inertial motion are added.
Quantum Gravity from General Relativity
The Routledge Companion to Philosophy of Physics, 2021
Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a quantum theory of gravity suggest that such a theory may have radical consequences for the nature, and indeed the fate, of spacetime. The present article articulates what this problem of spacetime is and traces it three approaches to quantum gravity taking general relativity as their vantage point: semi-classical gravity, causal set theory, and loop quantum gravity.