Related papers: An extension of the principle of relativity for on…
The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Accelerating cosmologies in extra dimensional spaces have been studied. These extra dimensional spaces are products of many spaces. The physical behaviors of accelerating cosmologies are investigated from Einstein's field equation in higher…
In this work, I examine spherically symmetric solutions in geometric sigma models with four scalar fields. This class of models turns out to be a subclass of the wider class of scalar-vector-tensor theories of gravity. The purpose of the…
The Regge-Teitelboim formulation of gravity, which utilizes dynamical embeddings in a background space, effectively introduces source terms in the standard Einstein equations that are not attributable to the energy-momentum tensor. We show…
We discuss non-relativistic conformal algebras generalizing the Schr\"odinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal…
A one-parameter generalized fermion algebra ${\cal B}_{\kappa}(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A…
We study 4d Friedmann-Lema\^{i}tre-Robertson-Walker cosmologies obtained from time-dependent compactifications of Type IIA 10d supergravity on various classes of 6d manifolds (Calabi-Yau, Einstein, Einstein-K\"{a}hler). The cosmologies we…
Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…
In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker…
The search for the physical mechanism underlying the observational evidence for the acceleration of the recent universe is a compelling goal of modern fundamental cosmology. Here we quantitatively study a class of homogeneous and isotropic…
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background…
For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
We propose a definition of uniform accelerated frames in de Sitter spacetimes applying the Nachtmann method of introducing coordinates using suitable point-dependent isometries. In order to recover the well-known Rindler approach in the…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change…
We examine models in which the accelerated expansion of the universe is driven by a scalar field rolling near an inflection point in the potential. For the simplest such models, in which the potential is of the form V(\phi) = V_0 + V_3…
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…