Related papers: Three-dimensional transformation for rotating coor…
In this paper, we review the recently formulated quantum laws of motion and provide new observations. We also extend these laws to higher dimensions. By applying in two dimensions the obtained relations to charge submitted to an electric…
We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
A new approach is developed to derive the complete spectrum of exact interdimensional degeneracies for a quantum three-body system in D-dimensions. The new method gives a generalization of previous methods.
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
The elliptic coordinates are used to build a new families of 2D coordinate systems which are orthogonal and admits the separation of variables. The charts of characteristic curves are constructed for these systems and compared with…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
In the theory of modern physics, such as in relativity and quantum mechanics, the three-dimensionality of space is introduced as a presupposed fact. The three-dimensionality of particle motion, that is, the three-dimensionality of particle…
A modified version of relational quantum mechanics is developed based on the three following ideas. An observer can develop an internally consistent description of the universe but it will, of necessity, differ in particulars from the…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…
Rotational energy dissipation in the solar system confines the planets to the ecliptic, this can be thought of as a dimensional reduction from three dimensions to two. It is argued that the same mechanism restricts five dimensional matter…
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem…
Preliminary results concerning non-quadratic (and non-bijective) transformations that exibit a degree of parentage with the well known Levi-Civita, Kustaanheimo-Stiefel, and Fock transformations are reported in this article. Some of the new…
Dynamics with noncommutative coordinates invariant under three dimensional rotations or, if time is included, under Lorentz transformations is developed. These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)…
Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi…
Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to…