arXiv subjects

Y. S. Kim

Publications and source records attributed to Y. S. Kim.

At least 91 records · Page 5Linked to original sources

arXiv2002

Internal Space-time Symmetries of Massless Particles and Neutrino Polarization as a Consequence of Gauge Invariance

There are gauge-transformation operators applicable to massless spin-1/2 particles within the little-group framework of internal space-time symmetries of massive and massless particles. It is shown that two of the $SL(2,c)$ spinors are invariant under gauge transformations while the remaining two are not. The Dirac equation contains only the gauge-invariant spinors leading to polarized neutrinos. It is shown that the gauge-dependent $SL(2,c)$ spinor is the origin of the gauge dependence of electromagnetic four-potentials. It is noted also that, for spin-1/2 particles, the symmetry group for massless particles is an infinite-momentum/zero-mass limit of the symmetry group for massive particles.

hep-th↗

arXiv2001

Wigner Rotations in Laser Cavities

The Wigner rotation is a key word in many branches of physics, chemistry and engineering sciences. It is a group theoretical effect resulting from two Lorentz boosts. The net effect is one boost followed or preceded by a rotation. This rotation can therefore be formulated as a product of three boosts. In relativistic kinematics, it is a rotation in the Lorentz frame where the particle is at rest. This rotation does not change its momentum, but it rotates the direction of the spin. The Wigner rotation is not confined to relativistic kinematics. It manifests itself in physical systems where the underlying mathematics is the Lorentz group. It is by now widely known that this group is the basic scientific language for quantum and classical optics. It is shown that optical beams perform Wigner rotations in laser cavities.

math-ph↗

arXiv2001

Lorentz Group in Feynman's World

R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a Lorentz-covariant picture of the parton model. It is shown first how the Lorentz group can be used for studying the internal space-time symmetries of relativistic particles. These symmetries are dictated by Wigner's little groups, whose transformations leave the energy-momentum four-vector of a given particle invariant. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted that the E(2)-like symmetry of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like little group for massive particles. It is shown that the formalism can be extended to cover relativistic particles with space-time extensions, such as heavy ions and hadrons in the quark model. It is possible to construct representations of the little group using harmonic oscillators, which Feynman et al. used for studying relativistic extended hadrons. This oscillator formalism allows us to show that Feynman's parton model is a Lorentz-boosted quark model. The formalism also allows us to explain in detail Feynman's rest of the universe which is contained in his parton picture.

hep-ph↗

arXiv2001

Internal Space-time Symmetries of Massive and Massless Particles and their Unification

It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom.

hep-th↗

arXiv2001

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.

physics.optics↗

arXiv2000

Symmetries Shared by Particle Physics and Quantum Optics

It is known that two coupled harmonic oscillators can support the symmetry group as rich as O(3,3) which corresponds to the Lorentz group applicable to three space-like and three time-like coordinates. This group contains many subgroups, including O(3), O(3,2), O(2,1) which are already familiar to us. In this report, we discuss the symmetry of O(1,1) which plays pivotal roles in quantum optics and particle physics. For this one-parameter group, a full-fledged group theory is not necessary, and we can start the discussion from the Hamiltonian of the coupled oscillator system. It is shown first that, from the group theoretical point of view, the squeeze state of light is a representation of this O(1,1) group. It is then shown that the same mathematical device supports three seemingly different ideas of Feynman, namely the parton model, the relativistic quark model for hadrons, and the ``rest of the universe'' in connection with the density matrix. If these three theories are combined, they produce a covariant picture of Feynman's parton model with a built-in decoherence mechanism.

math-ph↗

arXiv2000

Feynman's Entropy and Decoherence Mechanism

If we reduce coherence in a given quantum system, the result is an increase in entropy. Does this necessarily convert this quantum system into a classical system? The answer to this question is No. The decrease of coherence means more uncertainty. This does not seem to make the system closer to classical system where there are no uncertainties. We examine the problem using two coupled harmonic oscillators where we make observations on one of them while the other oscillator is assumed to be unobservable or to be in Feynman's rest of the universe. Our ignorance about the rest of the universe causes an increase in entropy. However, does the system act like a classical system? The answer is again No. When and how does this system appear like a classical system? It is shown that this paradox can be resolved only if measurements are taken along the normal coordinates. It is also shown that Feynman's parton picture is one concrete physical example of this decoherence mechanism.

quant-ph↗

arXiv2000

Binary Representations of ABCD Matrices

The ABCD matrix is one of the essential mathematical instruments in optics. It is the two-by-two representation of the group Sp(2), which is applicable to many branches of physics, including squeezed states of light, special relativity and coupled oscillators. It is pointed out that the shear representation is oriented to binary logic which may be friendly to computer applications. While this is a future possibility, it is known that para-axial lens optics is based on the shear representation of the Sp(2) group. It is pointed out that the most general form of the ABCD matrix can be written in terms of six shear matrices, which correspond to lens and translation matrices. The parameter for each shear matrix is computed in terms of the three independent parameters of the ABCD matrix.

physics.optics↗

arXiv2000

Further Contents of Einstein's E = mc^{2}

The energy-mass content of Einstein's E = mc^{2} is well known. For a fixed value of mass, E = mc^{2} is an energy-momentum relation which takes the form E = \sqrt{m^{2} + p^{2}}. This relation was formulated in 1905 for point particles. Since then, particles have become more complicated. They have internal space-time structures. Massive particles carry the package of internal variables including mass, spin and quarks, while massless particles have the package containing helicity, gauge variables, and partons. The question then is whether these two different packages of variables can be unified into one single covariant package as E = mc^{2} does for the energy-momentum relations for massive and massless particles. The answer to this question is YES.

quant-ph↗

arXiv2000

Interferometers and Decoherence Matrices

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 into six-parameter representations of the Lorentz group, as in the case of polarization optics where there are two orthogonal components of one light beam. It is shown that there are groups of transformations which leave the coherency or density matrix invariant, and this symmetry property is formulated within the framework of Wigner's little groups. An additional mathematical apparatus is needed for the transition from a pure state to an impure state. Decoherence matrices are constructed for this process, and their properties are studied in detail. Experimental tests of this symmetry property are possible.

quant-ph↗

arXiv1999

Two-pearl Strings: Feynman's Oscillators

String models are designed to provide a covariant description of internal space-time structure of relativistic particles. The string is a limiting case of a series of massive beads like a pearl necklace. In the limit of infinite-number of zero-mass beads, it becomes a field-theoretic string. Another interesting limit is to keep only two pearls by eliminating all others, resulting in a harmonic oscillator. The basic strength of the oscillator model is its mathematical simplicity. This encourages us to construct two-pearl strings for a covariant picture of relativistic extended particles. We achieve this goal by transforming the oscillator model of Feynman {\it et al.} into a representation of the Poincaré group. We then construct representations of the O(3)-like little group for those oscillator states, which dictates their internal space-time symmetry of massive particles. This simple mathematical procedure allows us to explain what we observe in the world in terms of the fundamental space-time symmetries, and the built-in covariance of the model allows us to use the physics in the rest frame in order to explain what happens in the infinite-momentum frame. It is thus possible to calculate the parton distribution within the proton moving light-like speed in terms of the quark wave function in its rest frame.

hep-ph↗

arXiv1999

Gauge Transformations on Massless Spin-1/2 Particles and Neutrino Polarization as a Consequence of Gauge Invariance

The two-by-two representation of the SL(2,c) group is for spin-1/2 particles. Starting from this two-by-two representation, it is possible to construct the four-by-four matrices for spin-1 particles. For massless particles, it is possible to construct four-potentials from two-component SL(2,c) spinors. Four potentials are subject to gauge transformations and are gauge-dependent. Then this gauge dependence necessarily comes from the two-component spinors which make up the four-potential. Then there must be a gauge-dependent spinor. This gauge-dependent spinor is discussed in detail. It is shown that neutrino polarization is a consequence of gauge invariance applicable to the two-by-two representation of the SL(2,c) group.

hep-th↗

arXiv1999

Space-time Symmetry Transformations of Elementary Particles realized in Optics Laboratories

The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations can generate group representations applicable to different branches of physics. It is pointed out that polarization optics can be formulated in terms of the six-parameter Lorentz group. This allows us to construct optical instruments corresponding to the subgroups of the Lorentz groups. It is shown possible to produce combinations of optical filters that exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions, which are manifestations of the internal space-time symmetries of massive and massless particles.

hep-th↗

arXiv1998

Separable Four-dimensional Harmonic Oscillators and Representations of the Poincaré Group

It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and one-dimensional wave function for time-like coordinate. It is then possible to construct a representation of the Poincaré group for a massive particles having the O(3) internal space-time symmetry in its rest frame. This oscillator can also be separated into two transverse components and the two-dimensional world of the longitudinal and time-like coordinates. The transverse components remain unchanged under Lorentz boosts, while it is possible to construct the squeeze representation of the $O(1,1)$ group in the space of the longitudinal and time-like coordinates. While the squeeze representation forms the basic language for squeezed states of light, it can be combined with the transverse components to form the representation of the Poincarè group for relativistic extended particles.

math-ph↗

arXiv1998

Lorentz Covariance and Internal Space-time Symmetry of Relativistic Extended Particles

The difference between Lorentz invariance and Lorentz covariance is discussed in detail. A covariant formalism is developed for the internal space-time symmetry of extended particles, especially in connection with the insightful observations Feynman made during the period 1969-72. A Lorentz-group formalism is presented for the harmonic oscillator model of Feynman, Kislinger and Ravndal, which was originally based on hadronic mass spectra. This covariant version allows us to construct a parton distribution function by Lorentz-boosting the oscillator wave function of a hadron at rest. The role of the time-separation variable is discussed in detail. It is shown that, due to our inability to make measurements on this variable, it belongs to Feynman's rest of the universe. Our failure to observe the rest of the universe leads to an increase in entropy.

hep-ph↗

arXiv1998

Covariant Model of Relativistic Extended Particles based on the Oscillator Representation of the Poincaré Group

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 group for massive particles starting from harmonic oscillator wave functions for the quark model. The resulting oscillator wave functions are covariant and can be Lorentz-boosted. It is thus possible to obtain the parton model by boosting the quark model. A review of Wigner's theory of the little groups is given. It is shown that the covariant oscillator wave functions become squeezed as as the system becomes boosted. It is shown also that the Lorentz-squeezed quark distribution exhibits the peculiarities of Feynman's parton model including the lack of coherence in the calculation of cross sections. A historical review of the concept of covariance is given.

hep-ph↗

arXiv1998

Spin-Landau Orbit Coupling in Units of the Flux Quantum Observed from Zeeman Splitting of a Quantum Wire Array

In Zeeman spectra of a GaAs-AlGaAs quantum wire array with superlattice period lp, the zero-field shift is found to increase in steps of (2 pi hbar/ e)lp^{-2} at the cyclotron radius Rc ~lp, lp/2, and lp/3. This shift, caused by spin-Landau orbit coupling and quantized in units of the flux quantum 2 pi hbar /e,is a manifestation of the gauge invariance, and the first observation of the flux quantization in a non-superconducting material.The quantum interference associated with the phase difference in the quantum barrier scattering is also reported.

cond-mat.mes-hall↗

arXiv1998

Squeezed States as Representations of Symplectic Groups

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, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.

physics.optics↗