21 citations · 77 across the 18 of their papers we have counts for
22 papers
Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics
Young S. Kim, Marilyn E. Noz
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be in…
Einstein's E = mc^2 derivable from Heisenberg's Uncertainty Relations
Sibel Baskal, Young S. Kim, Marilyn E. Noz
Heisenberg's uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Hei…
Poincaré Symmetry from Heisenberg's Uncertainty Relations
Sibel Baskal, Young S. Kim, Marilyn E. Noz
It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the group which is isomorphic to the Lorentz group applicable to one time-like…
Photons in the Quantum World
Sibel Baskal, Young S. Kim, Marilyn E. Noz
Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields…
Loop Representation of Wigner's Little Groups
Sibel Baskal, Young S. Kim, Marilyn E. Noz
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symme…
Symmetries of Massive and Massless Neutrinos
Y. S. Kim
Wigner's little groups are subgroups of the Lorentz group dictating the internal space-time symmetries of massive and massless particles. These little groups are like O(3) and E(2)…
Entangled Harmonic Oscillators and Space-time Entanglement
Sibel Baskal, Young S. Kim, Marilyn E. Noz
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It…
Lorentz Coherence and the Proton Form Factor
Young S. Kim
The dipole cutoff behavior for the proton form factor has been and still is one of the major issues in high-energy physics. It is shown that this dipole behavior comes from the coh…
Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
Sibel Baskal, Young S. Kim, Marilyn E. Noz
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp…
Entropy and Temperature from Entangled Space and Time
Young S. Kim, Marilyn E. Noz
Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bou…
Poincaré Sphere and a Unified Picture of Wigner's Little Groups
Y. S. Kim
It is noted that the Poincaré sphere for polarization optics contains the symmetries of the Lorentz group. The sphere is thus capable of describing the internal space-time symmetri…
Symmetries shared by the Poincaré Group and the Poincaré Sphere
Young S. Kim, Marilyn E. Noz
Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that…
Dirac Matrices and Feynman's Rest of the Universe
Young S. Kim, Marilyn E. Noz
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four matrices. These fifteen matrices ca…
Lorentz Group in Ray and Polarization Optics
S. Baskal, Y. S. Kim
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, par…
Lorentz Harmonics, Squeeze Harmonics, and their Physical Applications
Young S. Kim, Marilyn E. Noz
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 tra…
Feynman's Decoherence
Y. S. Kim, Marilyn E. Noz
Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to…
Interferometers and Decoherence Matrices
D. Han, Y. S. Kim, Marilyn E. Noz
It is shown that the Lorentz group is the natural language for two-beam interferometers if there are no decoherence effects. This aspect of the interferometer can be translated int…
Covariant Model of Relativistic Extended Particles based on the Oscillator Representation of the Poincaré Group
Y. S. Kim
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincaré group, it is possible to construct representations of the little gr…
Squeezed States as Representations of Symplectic Groups
D. Han, Y. S. Kim
It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon states. Since the O(3,2) group has many subgroups, ther…
Does Lorentz Boost Destroy Coherence?
Y. S. Kim
It is shown that the time-energy uncertainty relation can be combined into the position-momentum uncertainty relation covariantly in the quark model of hadrons. This leads to a Lor…
Neutrino Polarization as a Consequence of Gauge Invariance
Y. S. Kim
It is pointed out that there are gauge-dependent and gauge-independent spinors within the little-group framework for internal space-time symmetries of massless particles. It is sho…
Lorentz Boosts as Squeeze Transformations and the Parton Picture
Y. S. Kim
It was shown by Gribov, Ioffe, Pomeranchuk in 1966 and by Ioffe in 1969 that a space-time picture is needed for the Lorentz deformation of hadronic interaction region. It is shown…