2021
2020
2019
 Einstein's E = mc^{2} derivable from Heisenberg's Uncertainty Relations,
with Sibel Baskal and Marilyn Noz,
Quantum Reports [1(2)], 236  251 (2019),
doi:10.3390/quantum1020021,
arXiv:abs/1911.03818,
For pdf with sharper images, click here.
 Mathematical Devices for Optical Sciences.
with S. Baskal and M.E. Noz
IOP Book
available from the
amazon.com
 Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity,
Invited paper presented at the 26th
International Conference on Quantum Optics and Quantum Information
(Minsk, Belarus, May 2019),
arXiv.org/abs/1911.01642,
pdf with sharper images.
 Poincaré Symmetry from Heisenberg's Uncertainty Relations,
with S. Baskal and M. E. Noz,
Symmetry [11(3)], 236  267 (2019),
doi:10.3390/sym11030409,
arXiv: abs/1903.05348"> ArXiv.
 Click here for my Einstein page.
 Click here for the Lorentz group applicable
to optical sciences.
2018
 New Perspectives on
Einstein's
E = mc^{2,}
with Marilyn E. Noz,
World Scientific,
availabble from various sources.
 For the city of Bern, the birth place of
E = mc^{2},
click here.
2017

In physics, harmonic oscillators and twobytwo matrices never become outdated.

 Harmonic Oscillators and Twobytwo Matrices in Symmetry Problems in Physics,
Collection of the papers published in the Symmetry journal.
Click here
available from the
amazon.com.
 Photons in the Quantum World,
with S. Baskal and M. E. Noz,
Invited paper presented at the 15th International Conference on Squeezed States and
Uncertainty Relations (Jeju, South Korea, August 1217, 2017).
ArXiv.
 Loop Representation of Wigner's Little Groups,
with S. Baskal and M. E. Noz,
Symmetry [9](7), 97:122 (2017),
doi:10.3390/sym9070097.
ArXiv.
2016
2015
2014
 QCD. What else is needed for the proton structure function,
presented at the Hadron Structure and QCD: from Low to High
Eenegies (Gatchina, Russia, 2014).
ArXiv.
 Wigner’s SpaceTime Symmetries based on the TwobyTwo
Matrices of the Damped Harmonic Oscillators and
the Poincaré Sphere,
with S. Baskal and M. E. Noz,
Symmetry [6], 473  515 (2014),
doi: 10.3390/sym6030473.
ArXiv.
 Poincaré Sphere and a Unified Picture of Wigner's Little Groups,
Proceedings of Wigner 111, Colorful & Deep Symposium, edited by
S. Varro, P. Adam, T.S. Biro, G. G. Barnafoldi, and P. Levai,
EPJ Web of Conferences, [78], 01005:1  8 (2014),
doi10.151/ejpcon/20147801005.
ArXiv.
 Entropy and Temperature from Entangled Space and Time,
with M. E. Noz,
Phys. Sci. Int. J. [4], 1015  1039 (2014).
ArXiv.
 Lens optics and the continuity problems of the ABCD matrix,
with S. Baskal ,
J. Mod. Opt. [61], 161  166 (2014).
ArXiv.
2013
 Historical Approach to physics according to Kant, Einstein, and Hegel,
presented at the 32nd Congress of the Italian
Society of Historians of Physics and Astronomy (Rome, Italy, September 2012),
publshed in the "Physics, Astronomy, and Engineering. Critical Problems in the
History of Science and Society", edited by Raphael Pisano, Danilo Cappechi, and Anna
Lukesova (Scientia Socialis Press, Scientia Socialis, Siauliai, Lithuania, 2013),
pages 113  122.
ArXiv: https://arxiv.org/abs/1301.6091
pdf with sharper images.
 Symmetries shared by the Poincaré Group and Poincaré Sphere,
with Marilyn E. Noz,
Symmetry [5], 223  252 (2013).
doi:10.3390/sym5030233,
ArXiv.
 Lorentz Group in Ray and Polarization Optics,
with Sibel Baskal,
Chapter 9 in "Mathematical Optics: Classical, Quantum and Computational
Methods" edited by Vasudevan Lakshminarayanan, Maria L. Calvo, and Tatiana Alieva
(CRC Taylor and Francis, New York 2013), pages 303  349.
ArXiv.
2012
 Dirac Matrices and Feynman's Rest of the Universe,
with M. E. Noz,
Symmetry [4], 626  643 (2012).
ArXiv.
 Poincaré Sphere and Decoherence Problems,
presented at the Fedorov Memorial Symposium:
International Conference "Spins and Photonic Beams at Interface," dedicated
to the 100th anniversary of F.I.Fedorov (Minsk, Belarus, 2011).
ArXiv.
2011
 Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications,
with M. E. Noz,
Symmerty [3], 16  36 (2011).
ArXiv.



Click on each figure to enlarge it.

 Einstein's Hydrogen Atom
2nd International Conference on Multimedia Technology (July 2011)
in Hangzhou, China; Workshop on Physics and Mathematics.
IEEE Catalong No. CFP1153KPRT, [7], Part II, 6324  6329 (2011),
pdf.
ArXiv.
 Time separation as a hidden variable in the Copenhagen school of
quantum mechanics, in Advances in Quantum Theory,
with M. E. Noz,
AIP Conference Series, No.1327, 138  147 (2011).
ArXiv.
 Internal spacetime symmetries of particles derivable
from periodic systems in optics,
Optics and Spectroscopy [111], 731  737 (2011).
ArXiv.
 The Language of Twobytwo Matrices spoken by Optical Devices,
presented at the 19th International Conference on Composites or Nano Engineering,
Shanghai (China 2011).
ArXiv.
2010
 Internal Spacetime Symmetries according to Einstein, Wigner, Dirac, and Feynman,
with M. E. Noz,
presented at the Petrov Centennial Conference (Kazan 2010).
ArXiv.
 QCD's Partner needed for Mass Spectra and Parton Structure Functions,
Acta Physica Polonica B [2], 325  330 (2010).
ArXiv.
 Optical activities as computing resources for spacetime symmetries,
Journal of Modern Optics [57], 17  22 (2010).
AriXiv

Possible Minkowskian Language in Twolevel Systems,
Journal of Optics and Spectroscopy [108], 297  300 (2010).
ArXiv.
 One analytic form for four branches of the ABCD matrix,
with S. Baskal,
J. Mod. Opt. [57], 1251  1259 (2010).
ArXiv.
2009

ABCD matrices as similarity transformations of Wigner matrices and
periodic systems in optics,
with S. Baskal,
J. Opt. Soc. Am. A [26], 3049  2054 (2009).
ArXiv.
 Can the Quark Model Be Relativistic Enough to Include the Parton Model?
with M. E. Noz,
The Physics of Quarks: New Research (Horizons in World Physics, Volume 265),
edited by Nicolas L. Watson and Theo M. Grant,
Nova Science Publishers, Inc. (Hauppauge, NY, 2009). pages 139  162.
ArXiv.
2007
2006

Einstein's coordinate in philosophy.
My own philosophy.


 Einstein, Kant, and Taoism,
ArXiv.
 Lorentz Group for Finite Crystals,
with S. Baskal and E. Georgieva,
ArXiv.
 The Question of Simultaneity in Relativity and Quantum Mechanics,
with M. E. Noz,
in Quantum Theory: Reconsideration of Foundations III,
American Institute of Physics 073540301/06, pages 168178 (2006).
ArXiv.
 de Sitter group as a symmetry for optical decoherence,
with S. Baskal,
Journal of
Physics A [39], 7775  7788 (2006).
pdf.
ArXiv with a different title.
2005
 Standing Waves in the Lorentzcovariant World,
with M. E. Noz,
Foundations of Physics
[35], 1289  1305 (2005).
ArXiv.
 Rotations associated with Lorentz boosts,
with S. Baskal,
J. Phys. A [38], 6545  6556 (2005).
ArXiv.
 Coupled oscillators, entangled oscillators, and Lorentzcovariant Oscillators,
with M. E. Noz,
Jounal of Optics B:
Quantum and Semiclassical [7], s 459  467 (2005).
ArXiv.
 Harmonic Oscillators as Bridges between Theories: Einstein, Dirac,
and Feynman,
with M. E. Noz,
presented at the International Symposium on Interdisciplinary Science
(Natchitoches, Louisiana, October 2004),
Proceedings edited by A. Ludu,
AIP Conference Proceedings, CP755,
61  69 (2005).
ArXiv.
 The language of Einstein spoken by optical instruments,
Optics and Spectroscopy [99] (3),
443  446 (2005).
ArXiv.
2004
 Einstein, Wigner and Feynman: From E = mc ^{2} to Feynman’s
decoherence via Wigner’s little groups,
presented at the Wigner Centennial Conference held in Pecs,
Hungary (July 2002),
Acta Physica Hungarica A [19], 317318 (2004).
ArXiv.
 DashenFrautschi Fiasco and Historical Roadmap for Strings,
ArXiv.
 Is it possible to construct the Proton Structure Function by
Lorentzboosting the Static Quarkmodel Wave Function?
with M. E. Noz,
Int. J. Modern Phys. A [19], 5435  5442 (2004).
ArXiv.
 Lorentz group in ray optics,
with S. Baskal, E. Georgieva, and M. E. Noz,
Journal of Optics B: Quantum and Secmiclassical Optics [6]
S455  S472 (2004).
AriXiv.
2003



Feynman liked the Brazilian city of Rio de Janeiro, and he went there
very often. I went there in 2000 to see why he liked this city so much.
Click here for my
Feynman page.

 Feynman's Branes and Feynman's Oscillators,
presented at the Workshop on Branes and Generalized Dynamics
(Argonne, Illinois, USA, October 2003).
ArXiv.
 Is the concept of quantum probability consistent with Lorentz covariance?
with M. E. Noz,
presented at the Second International Conference on Foundations
of Probability in Physics (Vaxjo, Sweden, June 2002).
Proceedings edited by Andrei Khrennikov, Vaxjo University Press (Vaxjo 2002).
pages 345358.
ArXiv.
 Feynman's decoherence,
Optics and Spectroscopy [94], 733  740 (2003).
ArXiv.
 Lens optics as an optical computer for group contractions,
with S. Baskal,
Phys. Rev. E [67], 056601:1  6 (2003).
ArXiv.

Sliderulelike property of Wigner’s little groups
and cyclic S matrices for multilayer optics,
with E. Georgieva,
Phys. Rev. E [68], 026606: 1 7 (2003).
ArXiv.
 Wigner's new physics frontier: Physics of twobytwo matrices, including
the Lorentz group and optical instruments,
presented at various conferences during the year 2003.
ArXiv.
2002
 Lens optics and group contractions,
with S. Baskal,
Phys. Rev. E [67], 056601:1  7 (2002).
ArXiv.
 Wigner's spins, Feynman's partons, and their common ground,
based on one of the lectures delivered at the Advanced Study Institute
on Symmetries and Spin (Prague, Czech Republic, July 2001),
Czech.J.Phys. 52: C433  C442 (2002).
 ArXiv.
 Internal spacetime symmetries of massless particles and neutrino
polarization as a consequence of gauge invariance,
based on one of the lectures delivered at the Advanced Study Institute
on Symmetries and Spin (Prague, Czech Republic, July 2001),
Czech.J.Phys. 52: C353  C364 (2002).
ArXiv.
 Quarkparton phase transitions and the entropy problem in
quantum mechanics,
presented at International Conference on Quantum Electrodynamics and
Statistical Physics, dedicated to the 90th anniversary of
Alexander I. Akhiezer (Kharkov, Ukraine, Oct. 30  Nov. 3, 2001),
The Problems of Atomic Science and Technology,
Special Issue dedicated to the 90th Birthday Anniversary of
A. I. Akhiezer, No. 6 (1), 149  153 (2001).
ArXiv.
 Wigner rotations in laser cavities.
with S. Baskal,
Phys. Rev. E [66], 26604:1  6 (2002).
ArXiv.
2001
 Internal spacetime symmetries of massive and massless particles and
their unification,
prsented at the International Conference on Supersymmetry and Quantum Field
Theory, in commemoration of Dmitri Volkov's 75th Birthday, Kharkov, Ukraine, 2000),
Nuclear Physics (B  Proc. Suppl.) [102/103], 369  176.
ArXiv.
 Lorentz group in Feynman's world: Wignr's Little Groups and their
Applicationns,
with M. E. Noz,
in "Lorentz and Poincaré Invariance  100 Years in the Development
of Relativity," Pages 351  376,
edited by J. P. Hsu and P. Zhang (World Scientific, 2001).
ArXiv.
 Symmetries shared by particle physics and quantum optics,
presented at
the 23rd International Colloquium on Group Theoretical Methods in Physics
(Dubna, 2000).
ArXiv.
 Iwasawa effect in multilayer optics,
with E. Georgieva,
Phys. Rev. E [64], 026602: 16 (2001).
ArXiv.
 Shear representations of beam transfer matrices,
with S. Bakal,
Phys. Rev. E [63], 056606:1  6 (2001).
ArXiv.
(with a different title).
2000
 Feynman's entropy and decoherence problems,
presented at the 20th International Workshop on
Bayesian Inference and Maximum Entropy Methods in Science and Engineering,
(GifsurYvette, France 313 July 2000).
Proceedings edited by Ali MohammadDjafari,
AIP Conference Proceedings, Volume 568 (2001): pages 409417.
ArXiv.

Further contents of Einstein's E = mc^{2} ,
presented at the 4th International Conference on Geometrization of Physics
(Kazan, Russia, October, 1999).
ArXiv,
webpage.
 Interferometers and decoherence matrices,
with D. Han and M. E. Noz,
Phys. Rev. E [61], 5907  5913 (2000).
ArXiv.
1999
 Illustratative Example of Feynman's Rest of the Universe,
with D. Han and M. E. Noz,
Am. J. Phys. [67], 61  66 (1999),
pdf.
ArXiv.
 Gauge Transformations on Massless Spin1/2 Particles and Neutrino Polarization
as a Consequence of Gauge Invariance,
contribution to the Proceedings of International Workshop on "Lorentz Group,
CPT and Neutrinos" (Zacatecas, Mexico, June 2326, 1999).
ArXiv.
 Spacetime Symmetry Transformations of Elementary Particles
realized in Optics Laboratories,
presented at various conferences during the year 1999.
ArXiv.
 Wigner Rotations and Iwasawa Decompositions in Polarization Optics,
with D. Han and M. E. Noz,
Phys. Rev. E. [60], 1036  1041 (1999).
ArXiv.
 Twopearl Strings: Feynman's Oscillators (Protvino)
presented at the 22nd International Workshop on the Fundamental
Problems of High Energy Physics and Field Theory
(Protvino, Russia, June 1999).
ArXiv.
1998
 Does Lorentz boost destroy coherence?
Fortschr. der Physik [46], 713  724 (1998).
ArXiv.
 Lorentz Covariance and Internal Spacetime Symmetry of
Relativistic Extended Particles,
Contribution to the Nova Collection of papers
on the Lorentz group (edited by Valeri Dvoeglazov).
ArXiv.
 Covariant Model of Relativistic Extended Particles based on the
Oscillator Representation of the Poincaré Group,
contribution to the Volume dedicated to Prof. T.Y.Wu on his 90th Birthday
edited by J. P. Hsu and L. Hsu (World Scientific, Singapore, 1978).
ArXiv.

Separable Fourdimensional Harmonic Oscillators and Representations of
the Poincaré Group,
3rd International Workshop on Classical and Quantum Integrable
Systems (Yerevan, Armenia, 1998).
ArXiv.
 Wigner's photons,
presented at the 5th International Conference on Squeezed States and
Uncertainty Relations (Lake Balatonfured, Hungary, May 2731, 1997).
ArXiv.
 Squeezed States as Representations of Symplectic Groups,
presented at the 5th International Conference on Squeezed States and
Uncertainty Relations (Lake Balatonfured, Hungary, May 2731, 1997).
ArXiv.
1997
 Little groups and Maxwelltype tensors for massive and massless particles,
Euro. J. Phys. [47], 357  380 (1997).
ArXiv.
 Jones matrix formalism as a representation of the Lorentz group
J. Opt. Soc. Am. A [14], 2290  2298 (1997).
ArXiv.
 Stokes parameters as a Minkowskian fourvector,
with D. Han and M. E. Noz,
Phys. Rev. E [56], 6055  6076 (1997).
ArXiv.

 I met Erdal Inonu at a conference held in Instanbul (1997). The
younger person in this photo is Nikolaj Gromov. He was very
enthusiastic about group contractions at that time.
 Click here for my Wigner
page, and Einstein page.

 Group Contractions: Inonu, Wigner, and Einstein,
Int. J. Mod. Phys. A [12], 71  78 (1997).
ArXiv.
 Highspeed Contraction of Transverse Rotations to Gauge Transformations
presented at the International Workshop on Quantum Groups,
Deformations, and Contractions, Istanbul, Turkey (September 1997).
ArXiv.
 Wavlets and information preserving transformations,
Quantum Communication, Computing, and Measurement, edited by O. Hirota,
A. S. Holevo, and C. M. Caves (Plenum, New York, 1997). pages 119 126,
presented at the 3rd International Conference on Quantum Communications
and Measurements (FujiHakone Land, Japan, September, 1996).
ArXiv.
 Eugene Wigner and translation invariance (Poznan 96),
presented at the 4th International School on Theoretical Physics:
Symmetry and Structural Properties of Condensed Matter
(Zajaczkowo, Poland, AugustSeptember, 1996).
Proceedings edited by T. Lulek, W. Florek, and B. Lulek,
World Scientific (Singapore, 1997): pages 112.
ArXiv.
 Lorentz group in condensed matter physics (Poznan 96)
presented at the 4th International School on Theoretical Physics:
Symmetry and Structural Properties of Condensed Matter
(Zajaczkowo, Poland, AugustSeptember, 1996).
Proceedings edited by T. Lulek, W. Florek, and B. Lulek,
World Scientific (Singapore, 1997): pages 116127.
ArXiv.
1996
 Wigner's Last Papers on Spacetime Symmetries,
presnted at the 4th Wigner Symposium (Gudalajara, Mexico, 1995).
Proceedings edited by N. M. Atakisiev, T. H. Seligman,
K. B. Wolf (World Scientific, Singapore 1996): pages 110.
ArXiv.
 Wigner's Influence on Particle Physics: Unification
of Spacetime Symmetries of Massive and Massless Particles,
Acta Physica Polonica B [27], 2741  2746 (1996).
ArXiv.
 Lorentz Group derivable from Polarization Optics,
with M. E. Noz,
presented at the 21st International Colloquium on Group Theoretical Methods
in Physics (Goslar, Germany, July, 1996).
ArXiv.
 Polarization Optics and Bilinear Representations of the Lorentz Group,
with D. Han and M. E. Noz,
Phys. Lett. A [219], 26  32 (1996).
 Quantization and Spontaneous Emission in Circular Cylindrical
Cavities,
with K. Kakazu,
Prog. of Theor. Phys. [96], 883  899 (1996).
ArXiv.
 Lorentz Boosts as Squeeze Transformations and the Parton picture
J. Moscow Phys. Soc. [6], 45  58 (1996).
ArXiv.

Paul A. M. Dirac and his wife. She was Wigner's younger sister.

 Wigner's Sisters,
based on the preface of the Proceedings of the 4th Wigner
Symposium, edited by N. M. Atakisiev, T. H. Seligman,
K. B. Wolf (World Scientific, Singapore 1996).
Symposium (World Scientific, Singapore, 1996).
Webpage.
ArXiv.
 Neutrino Polarization as a Consequence of Gauge Invariance
pesented at the 2nd International Workshop on Quantum Systems
(Minsk, Belarus, May, 1996).
ArXiv.
 Lorentz Boosts as Squeeze Transformations and Coherence
Problems,
with D. Han
presented at the 4th Wigner Symposium (Guadalajara, Mexico, 1995).
Proceedings edited by N. M. Atakisiev, T. H. Seligman,
K. B. Wolf (World Scientific, Singapore 1996): pages 458461.
ArXiv.
 Lorentz Boosts as Squeeze Transformations and Coherence Problems,
with D. Han,
presented at the 4th Wigner Symposium (Gudalajara, Mexico, 1995).
ArXiv.
1995

Dirac's mathematical poem for two oscillators.
Click here for larger image.

 O(3,3)like Symmetries of Coupled Harmonic Oscillators,
with D. Han and M. E. Noz,
J. Math. Phsys. [36], 3940  3954 (1995).
ArXiv.
 Wavelets, Windows, and Photons,
with D. Han and M. E. Noz,
Phys. Lett. A [206], 299  304 (1995).
 Two Different Squeeze Transformations,
with D. Han,
presented at the 4th International Conference on Squeezed States
and Uncertainty Relations (Taiyuan, Shanxi, China, June 58, 1995).
ArXiv.
1994
1993
1992
1991
1990
 Spacetime geometry of relativistic particles
with E. P. Wigner,
J. Math. Phys. [31], 55  60 (1990).
pdf.
 Canonical transformation in quantum mechanics,
with E. P. Wigner,
Am. J. Phys. [58], 439  447 (1990).
 Linear Canonical Transformations of Coherent and Squeezed States
in the Wigner Phase Space III. Twomode States
with D. Han and M. E. Noz,
Phys. Rev. A [41], 6233  6244 (1990).
 Entropy and Lorentz Transformations,
with E. P. Wigner,
Phys. Lett. A [147], 343  346 (1990).
pdf.
 Lorentzsqueezed Hadrons and Hadronic Temperature,
eith D. Han and M. E. Noz,
Phys. Lett. A [144], 111  115 (1990).
pdf.
1989
 Observable Gauge Transformations in the Parton Picture
Phys. Rev. Lett. [63], 348  351 (1989).
pdf.
Einstein's World

Massive/Slow 
between 
Massless/Fast 

Energy Momentum 
E = p^{2}/2m 
Einstein's
E=(m^{2} + p^{2})^{1/2}

E = cp 


Hadrons, Bound States 
GellMann's Quark Model 
One LorentzCovariant Entity 
Feynman's Parton Picture 

This table is from
my PRL paper published in 1989.
Since I made a contribution to the 3rd row of the above table,
I am known as Wigner's student in the physics community.

 New observable effects of the Lorentz group,
with D. Han and E. Hardekopf,
Nucle. Phys. B (Proc. Suppl.) [6], 321  326 (1989).
 Squeezed states and thermally excited states in the wigner phasespace
picture of quantum mechanics,
with M. Li,
Phys. Lett. A [139], 445  448 (1989).
 Covariant phasespace representation and overlapping distribution
functions,
with E. P. Wigner,
Phys. Rev. A [39], 2829  2834 (1989).
 Linear canonical transformations of coherent and squeezed states
in the Wigner phase space. II. Quantitative analysis .
with D. Han, and M. E. Noz,
Phys. Rev. A [40], 902  912 (1989),
1988
 Linear canonical transformations of coherent and squeezed states in
the Wigner phase space,
with D. Han and M. E. Noz,
Phys. Rev. A [37], 807 – 814, (1988).
 Covariant phasespace representation for harmonic oscillators.
with E. P. Wigner,
Phys. Rev. A [38], 1159  1167 (1988).
 Special relativity and interferometers,
with D. Han,
Phys. Rev. A. [37], 4494  4495 (1988).
 Special Relativity and Quantum Theory,
with M. E. Noz,
Kluwer Academic Publshers (1988),
available from the
amazon.com
1987
 Cylindrical group and massless particles,
with E. P. Wigner,
J. Math. Phys. [28], 1175  1179 (1987).
pdf.
 Covariant phasespace representation for localized light waves,
with E. P. Wigner,
E. P. Wigner,
Phys. Rev. A [36], 1293 – 1297 (1987).
 Decomposition of Lorentz transformations,
with D. Han and D. Son,
J. Math. Phys. [28], 2373  2378 (1987).
 Thomas precession, Wigner rotations and gauge transformations,
with D. Han and D. Son,
Class. Quantum Grav. [4], 1777  1783 (1987).
 Uncertainty relations for light waves and the concept of photons,
with D. Han and M. E. Noz,
Phys. Rev. A [35], 1682  1691 (1987).
1986

In 1986, I was able to tell Eugene Wigner the stories he wanted to hear,
and he used to visit the Univ. of Maryland. John S. Toll was the chancellor
of the University at that time. He became very happy to meet Wigner.

 Photons, neutrinos, and gauge transformations,
with D. Han and D. Son,
Am. J. Phys. [54], 818  821 (1986).
 Eulerian Parametrization of Wigner's Little Groups and Gauge
Transformations in term of Rotations of Twocomponent Spinors,
with D. Han and D. Son,
J. Math. Phys. [27], 2228  2236 (1986).
pdf.
 Theory and Applications of the Poincaré Group,
with M. E. Noz,
Reidel, Dordrecht (1986),
Math. Rev.
available from the
amazon.com.
1985
1984
1983
 Gauge transformations as LorentzBoosted rotations,
with D. Han and D. Son,
Phys. Lett. B [131], 327  329 (1983).
Einstein's World

Massive/Slow 
between 
Massless/Fast 

Energy Momentum 
E = p^{2}/2m 
Einstein's
E=(m^{2} + p^{2})^{1/2}

E = cp 


 Massless composite particles and spacetime description of gauge transformations,
with D. Han and D. Son,
Phys. Rev. D [27], 2348  2353 (1983).
 cnumber timeenergy uncertainty relation in the quark model,
with D. Han, M. E. Noz, and D. Son,
Phys. Rev. D [27], 3032  3035 (1983).
 Illustrative examples of the symplectic group,
with M. E. Noz,
Am. J. Phys. [51], 368  375 (1983).
1982

Polarizations of massless neutrinos. Did you know they are consequences of the
gauge invariance on massless particles?

 E(2)like Little Group for Massless Particles and Polarization of Neutrinos,
with D. Han and D. Son,
Phys. Rev. D [26], 3717  3725 (1982).
 Photon Spin as a Rotation in Gauge Space,
with D. Han and D. Son,
Phys. Rev. D [25], 461  463 (1982).
 Spacetime Symmetries of Confined Quarks,
with D. Han, M. E. Noz, and D. Son,
Phys. Rev. D [25], 1740  1743 (1982).
 Little groups, the quark model and gauge transformations,
with D. Han, M. E. Noz, and D. Son,
Physica A [114], 197  199 (1982).
 Dirac’s lightcone coordinate system,
with M. E. Noz,
Am. J. Phys. [50], 721  724 (1982).
1981

How would Bohr's atom look to a moving obserber?

 Dirac's Form of Relativistic Quantum Mechanics
with D. Han,
Am. J. Phys. [49], 1157  1161 (1981).
 The Little Group for Photons and Gauge Transformations,
with D. Han,
Am. J. Phys. [49], 348  351 (1981).
 Symplectic Formulation of Relativistic Quantum Mechanics,
with M. E. Noz,
J. Math. Phys. [22], 2289  2293 (1981).
 Physical Principles in Quantum field Theory and Covariant Harmonic
Oscillators,
with M. E. Noz,
Found. of Phys. [11], 895  903 (1981).
1980
 Quark model in the quantum mechanics curriculum,
with P. E. Hussar and M. E. Noz,
Am. J. Phys. [48], 1043  1049 (1980).
 Lorentz deformation in the O(4) and lightcone coordinate systems,
with M. E. Noz,
J. Math. Phys. [21], 1224  1228 (1080).
 Yukawa's Approach and Dirac's Approach to Relativistic Quantum Mechanics,
with M. E. Noz,
Progr. Theor. Phys. [64], 1852  1860 (1980).
pdf.
 Lorentz Deformation and the Jet Phenomenon II: Explanation of the
Nearly Constant Transverse Jet Phenomenon
with M. S. Noz and S. H. Oh,
Found. of Phys. [10], 635  639 (1980).
 Threeparticle symmetry classifications according to the method of Dirac,
with P. E. Hussar and M. E. Noz,
Am. J. Phys. [48], 1038  1042 (1980).
1979
 Representations of the Poincaré group for relativistic extended particles,
with M. E. Noz and S. H. Oh,
J. Math. Phys. [20], 1341  1344 (1979).
pdf,
pdf plus
Physics Auxiliary Publication Service.
The Gaussian entanglement is contained in this publicaction, and was
reintroduced in the following paper.
 A simple method for illustrating the difference between the
homogeneous and inhomogeneous Lorentz groups,
with M. E. Noz and S. H. Oh,
Am. J. Phys. [47], 892  897 (1979).
 Physical basis for minimal timeenergy uncertainty relation,
with M. E. Noz,
Found. of Phys. [9], 375  387 (1979).
 Lorentz Deformation and the Jet Phenomenon,
with M. E. Noz and S. H. Oh,
Found. of Phys. [9], 947  954 (1979).
 Lorentz Deformation of the BetheSalpeter Wave Function,
with M. E. Noz, Hadronic J. [2], 460  480 (1979).
1978
 Relativistic harmonic oscillators and hadronic structures in the
quantummechanics curriculum,
with M. E. Noz,
Am. J. Phys. [46], 484  488 (1978).
 Quarks, Partons and LorentzDeformed Hadrons,
with M. E. Noz,
Progr. Theor. Phys. [60], 801  816 (1978).
 Group theory of covariant harmonic oscillators,
with M. E. Noz,
Am. J. Phys. [46], 480  483 (1978).
 Covariant Form of the Uncertainty Relations,
J. Kor. Phys. Soc. [11], 1  5 (1978).
1976
1975
 Smatrix, Wave Functions, and Foundations of Quantum Mechanics,
New Physics [15], 46  54 (1975).
 Covariant Harmonic Oscillators and Diffractive Excitations,
with M. E. Noz,
Phys. Rev. D [12], 122  128 (1975).
 Covariant Harmonic Oscillators and Excited Meson Decays,
with M. E. Noz,
Phys. Rev. D [12], 129  138 (1975).
1974
1973
 Covariant harmonic oscillators and the quark model,
with M. E. Noz,
Phys. Rev. D. [8], 3521  3526 (1973).
 Radial Effects in the Symmetric Quark Model,
with T. De and M. E. Noz,
Nuovo Cimento [13A], 1089  1101 (1973).
 It took 1000 years for human brains to realize the circle is
a special case of the ellipse.
 Einstein formulated his special theory of relativity more than
100 years ago based on Lorentz transformations, yet it is not easy
for physicists to see that the Lorentz boost is a squeeze
transformation.
1972
1971
1969
1968
1967
1966
1965
 Analytic Property of Threebody Unitarity Integral,
with J. N. Islam,
Phys. Rev. [138], B1222  B1230 (1965).
 Particlemixture Theory and Apparent CP Violation in Kmeson Decay,
with H. Ezawa, S. Oneda, and J. C. Pati,
Phys. Rev. Lett. [14], 673  676 (1965).
 Betadecay Coupling Constants,
Nuovo Cimento [36], 523  532 (1965).
 Role of Partially Conserved Axial Vector current in $\pi$ and K
Decays, with S. Oneda,
Progr. Theor. Phys., Special Issue Dedicated to
Professor H. Yukawa, 238  249 (1965).
1964
 Unitary Symmetry and Nonleptonic Kdecay,
with S. Oneda,
Phys. Lett. [8], 83  85 (1964).
 The omegaphi Mixing Angle,
with S. Oneda and J. C. Pati,
Phys. Rev. [135], B1076  B1079 (1964).
 Finalstate Interactions in the \eta to 3\pi Decay,
with S. Oneda and L. M. Kaplan,
Nuovo Cimento [34], 655  664 (1964).
 ThreeParticle Unitarity Integral,
Phys. Rev. [135], B454  B458 (1964).
 SU(3) Symmetry and the Nonleptonic Kmeson Processes,
with S. Oneda and D. Korff,
Phys. Rev. [136], B1064  B1073 (l964).
1963
1962
 Pion Production in the Lowenergy Limit,
Phys. Rev. [125], 1771  1777 (l962).
 Complex Angular Momentum in Twochannel Problems,
with A. M. Jaffe,
Phys. Rev. [127], 2261  2266 (1962).
 I came to the Univ. of
Maryland in July of 1962, and I was assigned to be a personal
assistant to Paul A. M. Dirac who visited Maryland for one week
in October of 1962. Thus, I had a Godgiven chance to talk and
listen to Dirac. Click here for
a detailed story.
1961
