Related papers: Dual Quantum Mechanics
It is shown that a unified description of classical and `quantum mechanical' gravity in its linearized form is possible.
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
It is shown that the Fourier transformation that relates position and momentum representations of quantum mechanics can be understood as a consequence of a symmetry principle that establishes the equivalence of being and becoming in the…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
We analyze the problem of general covariance for quantum gravity theories in the background field formalism with respect to gauge fixing procedure. We prove that the background effective action is not invariant under general coordinate…
In the present article, we construct a 2D formulation of quantum gravity in the framework of a deterministic theory. In this context, a Quantum stationary Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in the…
We propose a new approach to the quasitopological theory of gravity based on a modified classical double--copy construction. Focusing on static, spherically symmetric configurations, we show that all vacuum solutions of $D$--dimensional…