Related papers: Plausible "faster-than-light" displacements in a t…
Over the past few years, evidence has begun to accumulate suggesting that spacetime may undergo a "spontaneous dimensional reduction" to two dimensions near the Planck scale. I review some of this evidence, and discuss the (still very…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac…
We consider discrete spacetime models known as quantum walks, which can be used to simulate Dirac particles. In particular we look at fermion doubling in these models, in which high momentum states yield additional low energy solutions…
We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin $1/2$ moving in the three-dimensional Euclidean space. In this paper,…
The modification to four--dimensional Einstein gravity at low energy in two brane models is investigated within supergravity in singular spaces. Using perturbation theory around a static BPS background, we study the effective…
In a recent paper [1], it has been proposed that relativistic wave-particle duality can be embodied in a relation that shows that the four-velocity of a particle is proportional to the Dirac four-current. In this note we bring out some…
We consider discretized gravity in six dimensions, where the two extra dimensions have been compactified on a hyperbolic disk of constant curvature. We analyze different realizations of lattice gravity on the disk at the level of an…
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be…
In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We study various dualities in condensed matter systems. The dualities in three dimensions could be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at the Wilson-Fisher fixed point…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the…
This study delves deeply into braneworld scenarios within modified gravity models, investigating their impact on particle localization and the structure of branes. Through a comprehensive blend of numerical analyses and theoretical…
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac…
Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the…
We construct an intersecting brane configuration in six-dimensional space with one extra space-like and one extra time-like dimensions. With a certain additional symmetry imposed on the extra space-time we have found that effective…
In this thesis we study physics beyond the standard model focusing on the quantum field theory in higher-dimensional space-time with some boundary terms. The boundary term causes nontrivial consequences about the vacuum structure of the…