Related papers: Cube or hypercube of natural units
Let M be a compact Kahler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M//G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515--538]…
The newly discovered principle of maximum force makes it possible to summarize special relativity, quantum theory\se, and general relativity in one fundamental limit principle each. The three principles fully contain the three theories and…
The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…
A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
In spite of its outstanding success, quantum mechanics remains mysterious, many problems such as wave/particle dualism and quantum nonlocality remain open. Because a particle, e.g. a photon, is a quantum of a corresponding quantum field, an…
In this paper, we want to make to see the convenience of the amplification of the Planck`s system of absolute units through the introduction of two new constant, the dynamical constant and the permitividad of the vacuum upon rejecting that…
Very recently authors in [5] proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this Letter the effect of this GUP is studied in quantum cosmological models with dust and cosmic string as the…
This paper is the first of several parts introducing a new powerful algebra: the algebra of the pseudo-observables. This is a C*-algebra whose set is formed by formal expressions involving observables. The algebra is constructed by applying…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
Chaput, Manivel and Perrin proved a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we link this formula to…
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
The transition from the quantum to the classical world and its relation to Bose-Einstein condensation and superfluidity is explained in ten equations.
We consider algebras of $m\times m\times m$-cubic matrices (with $m=1,2,\dots$). Since there are several kinds of multiplications of cubic matrices, one has to specify a multiplication first and then define an algebra of cubic matrices…
We reconsider theories with low gravitational (or string) scale M_* where Newton's constant is generated via new large-volume spatial dimensions, while Standard Model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds…
IceCube, a cubic kilometer neutrino telescope will be capable of probing neutrino-nucleon interactions in the ultrahigh energy regime, far beyond the energies reached by colliders. In this article we introduce a new observable that combines…
In the scientific literature the equation $Q=\{Q\}[Q]$ is frequently quoted, where $Q$ denotes a quantity, $\{Q\}$ a numerical value, and $[Q]$ a unit. During the last years some experts claimed, that this equation is due to James Clerk…
Naturalness has for many years been a guiding principle in the search for physics beyond the Standard Model, particularly for understanding the physics of electroweak symmetry breaking. However, the discovery of the Higgs particle at 125…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…