arXiv subjects

Y. S. Kim

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

At least 109 records · Page 6Linked to original sources

arXiv1998

Wigner's Photons

If Einstein's photon is $E = cp = \hbarω$, Wigner's photon is its helicity which is a Lorentz-invariant concept coming from the E(2)-like little group for massless particles. In addition, the E(2)-like little group has two translation-like degrees of freedom. What happens to them? They are associated with the gauge degree of freedom. Since the physics of polarized light waves can be formulated within the framework of the Lorentz group, it is now possible to use polarization experiments to study the E(2)-like little group in terms of quantities that can be measured in laboratories.

hep-th↗

arXiv1997

High-speed Contraction of Transverse Rotations to Gauge Transformations

The Inonu-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of the cylindrical group and the two-dimensional Euclidean group. The Euclidean component becomes the Lorentz condition applicable to the electromagnetic four-potential, and the cylindrical component leads to the helicity and gauge degrees of freedom. The rotation around the cylindrical axis corresponds to the helicity, while the translation parallel to the axis on the cylindrical surface leads to a gauge transformation.

hep-th↗

arXiv1997

Does Lorentz Boost Destroy Coherence?

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 Lorentz-invariant form of the uncertainty relations. This model explains that the quark model and the parton model are two different manifestations of the same covariant model. In particular, this covariant model explains why the coherent amplitudes in the quark model become incoherent, after a Lorentz boost, in the parton model. It is shown that this lack of coherence is consistent with the present form of quantum mechanics.

quant-ph↗

arXiv1997

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.

physics.optics↗

arXiv1997

Coupled Harmonic Oscillators and Feynman's Rest of the Universe

According to Feynman, the universe consists of two parts - the system in which we are interested and the rest of the universe which our measurement process does not reach. Feynman then formulates the density matrix in terms of the observable world and the rest of the universe. It is shown that coupled harmonic oscillators can serve as an illustrative example for Feynman's ``rest of the universe.'' It is pointed out that this simple example has far-reaching consequences in many branches of physics, including statistical mechanics, measurement theory, information theory, thermo-field dynamics, quantum optics, and relativistic quantum mechanics. It is shown that our ignorance of the rest of the universe increases the uncertainty and entropy in the system in which we are interested.

cond-mat.stat-mech↗

arXiv1997

O(3,3)-like Symmetries of Coupled Harmonic Oscillators

In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or SL(4,r) in the four-dimensional phase space consisting of two position and two momentum variables. In quantum mechanics, the symmetry is reduced to that of O(3,2) or Sp(4), which is a subgroup of O(3,3) or SL(4,r) respectively. It is shown that among the six Sp(4)-like subgroups, only one possesses the symmetry which can be translated into the group of unitary transformations in quantum mechanics. In quantum mechanics, there is the lower bound in the size of phase space for each mode determined by the uncertainty principle while there are no restriction on the phase-space size in classical mechanics. This is the reason why the symmetry is smaller in quantum mechanics.

quant-ph↗

arXiv1997

Jones-matrix Formalism as a Representation of the Lorentz Group

It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the three-parameter rotation subgroup and the three-parameter Lorentz group for two spatial and one time dimensions. It is noted that the Lorentz group has another three-parameter subgroup which is like the two-dimensional Euclidean group. Possible optical filters having this Euclidean symmetry are discussed in detail. It is shown also that the Jones-matrix formalism can be extended to some of the non-orthogonal polarization coordinate systems within the framework of the Lorentz-group representation.

physics.optics↗

arXiv1997

Wigner's Sisters

Paul A. M. Dirac was a great physicist. Wigner used to call him ``my famous brother-in-law''. How did they become brothers-in-law? Did these two great physicists have the same view toward physics?

physics.hist-ph↗

arXiv1997

Lorentz Group derivable from Polarization Optics

The Lorentz group is the fundamental language for space-time symmetries of relativistic particles. This group can these days be derived from the symmetries observed in other branches of physics. It is shown that this group can be derived from optical filters. The group O(2,1) is appropriate for attenuation filters, while the O(3) group describes phase-shift filters. The combined operation leads to a two-by-two representation of the six-parameter Lorentz group. It is shown also that the bilinear representation of this group is the natural language for the polarization optics.

hep-th↗

arXiv1996

Eugene Wigner and Translational Symmetries

As Einstein's $E = mc^{2}$ unifies the energy-momentum relation for massive and massless particles, Wigner's little group unifies their internal space-time symmetries. It is pointed out that translational symmetries play essential roles both in formulating the problem, and in deriving the conclusions. The input translational symmetry is the space-time translation, and the output translational symmetry is built in the E(2)-like little group for massless particles. The translational degrees of freedom in this little group are gauge degrees of freedom. It should be noted that a number of condensed matter physicists played important supporting and supplementary roles in Wigner's unification of internal space-time symmetries of massive and massless particles.

cond-mat↗

arXiv1996

Lorentz Group in Condensed Matter Physics

It is shown that the Lorentz group plays prominent roles in at least two areas in condensed matter physics, namely in the Bogoliubov transformation and optical filters. It is pointed out that the underlying symmetry of the Bogoliubov transformation is that of two coupled oscillators, and that the underlying symmetry of two coupled oscillators in that of the group $O(3,3)$. The Lorentz group is also shown to be the underlying symmetry group for the Jones matrix formalism which is standard language for optical filters.

cond-mat↗

arXiv1996

Group Contractions: Inonu, Wigner, and Einstein

Einstein's $E = mc^{2}$ unifies the momentum-energy relations for massive and massless particles. According to Wigner, the internal space-time symmetries of massive and massless particles are isomorphic to $O(3)$ and $E(2)$ respectively. According to Inonu and Wigner, $O(3)$ can be contracted to $E(2)$ in the large-radius limit. It is noted that the $O(3)$-like little group for massive particles can be contracted to the $E(2)$-like little group for massless particles in the limit of large momentum and/or small mass. It is thus shown that transverse rotational degrees of freedom for massive particles become contracted to gauge degrees of freedom for massless particles.

hep-th↗

arXiv1996

Wavelets and Information-preserving Transformations

The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a Lorentz-covariant cut-off procedure. The window plays the central role in tackling the problem of photon localization. It is possible to make a transition from light waves to photons through the window. On the other hand, the windowed wave function loses analyticity. This loss of analyticity can be measured in terms of entropy difference. It is shown that this entropy difference can be defined in a Lorentz-invariant manner within the framework of the wavelet formalism.

quant-ph↗

arXiv1996

Neutrino Polarization as a Consequence of Gauge Invariance

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 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.

hep-th↗

arXiv1996

Lorentz Boosts as Squeeze Transformations and the Parton Picture

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 that this deformation is a squeeze transformation. It is shown also that Feynman's parton picture emerges as a consequence of Lorentz-squeezed hadrons in the quark model.

hep-ph↗

arXiv1996

Lorentz Boosts as Squeeze Transformations and Coherence Problems

The quark model and the parton model are known to be two different manifestations of the same covariant entity. However, the interaction amplitudes of partons are incoherent while they are coherent in the quark model. According to Feynman, this is due to the dilation of the interaction time among the quarks. We present a quantitative analysis of this time-dilation problem using Lorentz boosts as squeeze transformations.

hep-ph↗

arXiv1996

Two Different Squeeze Transformations

Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.

hep-th↗

arXiv1996

Unification of Spacetime Symmetries of Massive and Massless Particles

The internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The $O(3)$-like little group for a massive particle at rest and the $E(2)$-like little group of a massless particle are two different manifestations of the same covariant little group. Likewise, the quark model and parton pictures are two different manifestations of the one covariant entity.

hep-th↗