Related papers: Scaling-Based Quantization of Spacetime Microstruc…
We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained…
Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional…
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
It is proposed that gravity may arise in the low energy limit of a model of matter fields defined on a special kind of a dynamical random lattice. Time is discretized into regular intervals, whereas the discretization of space is random and…
A fundamental element of scale-dependent gravity is the scale-setting procedure. We present a new covariant expression to set the scale that arises when examining the field equations. Considering the renormalization group equations and…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…
A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
There are good indications that fundamental physics gives rise to a modified space-momentum uncertainty relation that implies the existence of a minimum length scale. We implement this idea in the scalar field theory that describes density…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, written using a modular-parameter normalization of size $2\pi$, that balances the geometric entropy increment $\delta A/4G$ against a reversible…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
We discuss the way of solving the hierarchy problem. We show that starting at the Planck scale, the three energy scales -- inflationary, electroweak and the cosmological ones can be restored. The formation of small parameters is proposed…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
In addressing the cosmological constant problem, we propose that the discrepancy between the theoretical and observed values can be ascribed to the inherent uncertainty in the spacetime metric. Mach's principle, which posits that mass…
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group…