Related papers: Loop Quantum Mechanics and the Fractal Structure o…

We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic…

The concept of the quantized space-time of the formless finite fundamental elements is suggested. This space-time can be defined as a set of continual space-time coverings by simply connected non-overlapping regions of any form and…

We perform a detailed comparison of the dynamics of cosmic string loops obtained in cosmological field theory simulations with their expected motion according to the Nambu-Goto action. We demonstrate that these loops follow the trajectories…

We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on…

Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…

In this paper we show that, via an extension of time, some metric structures naturally appear in both classical and quantum mechanics when both are formulated via path integrals. We calculate the various Ricci scalar and curvatures…

Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…

Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…

We review some aspects of Nambu mechanics on the basis of the works previously published separately by the present author. Main focuses are on three themes, its various symmetry structures, their possible relevance to string/M theory, and a…

The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…

In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been…

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…

We study the dynamics of Nambu-Goto cosmic string loops coupled to a massive Kalb-Ramond field. This coupling provides a framework for describing the interaction between the cosmic string and the gauge field. Within this setup, we compute…

We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto…

We review the status of understanding of the fractal structure of the quantum spacetime of 2d gravity coupled to conformal matter with c <= 1, with emphasis put on the results obtained last year.

We propose a modification of the Nambu-Goto action for the bosonic string which is compatible with the existence of a minimum area at the Planck scale. The result is a phenomenological action based on the observation that LQG tells us that…

This work explores the possibility of applying stochastic quantum mechanics to curved spacetimes, with an emphasis on the Schwarzschild black hole. After reviewing the fundamental concepts of this approach, the quantum stochastic equations…

Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…