Related papers: Interpreting the Kustaanheimo-Stiefel transform in…
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional…
We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on…
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion,…
The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is…
The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan space-time and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass…
It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
The observed large-scale structure in our Universe is seen as a result of quantum fluctuations amplified by spacetime evolution. This, and related problems in cosmology, asks for an understanding of the quantum fields of the standard model…
In a recent proposal using the group field theory approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of "atoms of space," which allows the derivation of an effective cosmological…
Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics,…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory…
We consider supersymmetric theories with a warped extra dimension where supersymmetry is broken by boundary conditions that preserve an R-symmetry. It is shown that this supersymmetry breaking mechanism naturally invokes the Stuckelberg…
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric…
In this work, we explore the de Broglie-Bohm Quantum Cosmology for a stiff matter, $p = \rho$, anisotropic n-dimensional Universe. One begins by considering a Gaussian wave function for the Universe, which depends on the momenta parameters…
By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation…
In this note, we present the Kustaanheimo-Stiefel regularization in a symplectic and quaternionic fashion. The bilinear relation is associated with the moment map of the $S^{1}$- action of the Kustaanheimo-Stiefel transformation, which…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore,…