相关论文: Klein-Gordon-Langevin Quantum Geometry
We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the Null-Surface Formulation of general relativity, recently developed, with asymptotic…
We consider the motion of a massive particle in a static, weakly-curved spacetime where the gravitational field is taken to be quantized. We find that Newton's law of free-fall is modified by quantum-gravitational corrections, in addition…
We quantize a real massive Klein-Gordon field in curved spacetimes within the general boundary formulation. The vacuum wave function is given by a Gaussian in the Schr\"odinger representation and we study the general structure of the…
We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Fr\"olicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position…
The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…
Performing a relativistic approximation as the generalization to a curved spacetime of the flat space Klein-Gordon equation, an effective Hamiltonian which includes non-minimial coupling between gravity and scalar field and also quartic…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states…
In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics.…
Stochastic field equations for linearized gravity are presented. The theory is compared with the usual quantum field theory and questions of Lorentz covariance are discussed. The classical radiation approximation is also presented.
We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
We discuss the Schwartz-Meyer second order geometry framework and its relevance to theories of quantum gravity that incorporate a notion of spacetime stochasticity or quantum foam. We illustrate the framework in the context of Nelson's…
In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because…