Semiclassical approximation to supersymmetric quantum gravity (original) (raw)

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

Quantum gravity: an introduction to some recent results

Reviews of Modern Physics, 1989

This article presents a general overview of the problems involved in the application of the quantum principle to a theory of gravitation. The ultraviolet divergences that appear in any perturbative computation are reviewed in some detail, and it is argued that it is unlikely that any theory based on local quantum fields could be consistent. This leads in a natural way to a supersymmetric theory of extended objects as the next candidate theory to study. An elementary introduction to superstrings closes the review, and some speculations about the most promising avenues of research are offered. CONTENTS Gravitational Fields III. Einstein Gravity as a Gauge Theory. Perturbative Results at One and Two Loops A. Gravity as a gauge theory B. The method of the background field C. The one-loop computation of 't Hooft and Veltman D. The two-loop computation of Goro6'and Sagnotti IV. Ultraviolet Divergences in a Quantum Field Theory of Gravity V. Canonical Formalism: The Wheeler-De%'itt Equation VI. The Semiclassical Approximation: Schrodinger s Equation VII. Some Specific Boundary Conditions. Toy Models in Quantum Cosmology A. The de Sitter model of Hartle and Hawking B. The effect of conformally invariant scalars in the toy model C. A cosmological model of Banks VIII. Quantum Gravity in the General Framework of Superstring Theories A. Gravity from strings B. Modular invariance C. Gravity in the long-wavelength limit D.

Note on the semiclassical approximation in quantum gravity

Physical Review D, 1996

We re-examine the semiclassical approximation for quantum gravity in the canonical formulation, focusing on the definition of a quasiclassical state for the gravitational field. It is shown that a state with classical correlations must be a superposition of states of the form e iS . In terms of a reduced phase space formalism, this type of state can be expressed as a coherent superposition of eigenstates of operators that commute with the constraints and so correspond to constants of the motion. Contact is made with the usual semiclassical approximation by showing that a superposition of this kind can be approximated by a WKB state with an appropriately localised prefactor. A qualitative analysis is given of the effects of geometry fluctuations, and the possibility of a breakdown of the semiclassical approximation due to interference between neighbouring classical trajectories is discussed. It is shown that a breakdown in the semiclassical approximation can be a coordinate dependent phenomenon, as has been argued to be the case close to a black hole horizon.

Dirac-like formulation of quantum supersymmetric cosmology

Physical Review D, 1998

We present a Dirac-like framework for quantum cosmology. This is achieved by representing the gravitino field components, analogously to the Dirac equation, as matrices. In particular, we work out the Bianchi type IX diagonal model. The Lorentz constraints J ␣␤ can then be applied explicitly on the wave function, which results in a 64-component vector, without any particular assumption on its expansion in fermionic ͑and bosonic͒ variables. The resulting wave function has only two nonvanishing components. Hence, the Dirac-like structure of the S A constraints manifests itself in a system of equations for these two functions, where the ''potential'' plays the role of the charge in Dirac's theory. We exhibit two solutions whose explicit form is determined by the chosen factor ordering. The proposed construction can be systematically extended to other cosmologies and the inclusion of matter.

Hamilton–Jacobi Wave Theory in Manifestly-Covariant Classical and Quantum Gravity

Symmetry, 2019

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder-Weyl variational formulation (2015-2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable g µν being realized by the third-order 4-tensor Π α µν. It is shown that this generates a corresponding Hamilton-Jacobi theory in which the Hamilton principal function is a 4-tensor S α. However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton-Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field.

Quantum Gravity Equation In Schrödinger Form In Minisuperspace Description

General Relativity and Gravitation

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.

The Quantum Gravity Lagrangian

2013

  1. 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.

Classical and quantum general relativity: A new paradigm

General Relativity and Gravitation, 2005

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.

Quantum theory requires gravity and superrelativity

1996

The ordinary quantum theory points out that general relativity is negligible for spatial distances up to the Planck scale. Consistency in the foundations of the quantum theory requires a``soft'' spacetime structure of the general relativity at essentially longer length. However, for some reasons this appears to be not enough. A new framework (``superrelativity'') for the desirable generalization of the foundation of quantum theory is proposed. A generalized non-linear Klein-Gordon equation has been derived in order to shape a stable wave packet.