green bay packerscheap oakely sunglassescheap uggscheap uggs outletUgg Classic Mini 5854UGG Metallic Short 5842UGG Classic Short 5800UGG Classic Short 5281UGG Bailey Button 5991UGG Classic Short 5251Mulberry Alexa BagsMulberry Bayswater BagsMulberry Bagscheap Mulberry HandBagswashington redskins jerseyscustom washington redskins jerseys
ELECTROMAGNETIC PHENOMENA   2006, Vol.6, No.2(17)  121-123


Editorial Introduction


This special issue is based on scientific research works presented at the Workshop "Mathematical Physics: Symmetries" (Zacatecas, México, December 1-2, 2005). Among the authors the reader will find the well-known names of Profs. N. V. Mitskievich, M. Socolovsky, M. Napsuciale, A. Gutiérrez-Rodríguez, Z. Oziewicz, J. Keller, R. Alvarado Flores, J.A. Pérez, J. Martínez Ortiz, H. Rosu and J.P. Treviño, M. Agüero Granados, A. Enciso Muñoz. Several participants (A.E. Chubykalo, V.V. Dvoeglazov, A. Espinoza Garrido, V. Kravchenko, H. Oviedo, A.I. Nesterov) had their presentations published with other Journals before the Workshop. This Workshop continued the series of the small Workshops organized in 2005 by various Mexican Universities on the subjects of SUSY, neutrinos and flavor in the particle theory. The Workshop being announced as national, in fact, it was truly international, because many of its participants came from Eastern Europe to México as visiting scientists in the 90s. The topic "Symmetries" is of interest to several faculty members of the Zacatecas Physics School, while other events (held in 1999 and 2000) were also related to. We invited experts in group theory, non-associative algebras, category theory, differential geometry, non-linear theories, classical field theory, gauge theories, spin, etc in order to provide further impetus to these research areas at the Zacatecas University and in M\'exico altogether (the attention paid to them here is not yet sufficient).

Let us review briefly the papers included in this volume. The Mitskievich paper begins with a statement that "it seems that everybody knows what the electromagnetic field is". On the other hand, in the text we find the following statements, "gravitation does automatically regularize the global characteristics so that in general relativity local singularities do not anymore lead to an integral energy divergence" (remember the well-known Einstein problems of constructing the unified field theory?); "in 2 + 1 [dimension] field constructed from the vector (rank 1) potential ... essentially has properties of a fluid and not of electromagnetic field..."; "a complete elimination of the pure null type field is 'possible' only asymptotically"; "in the impure case it is impossible to transform away the counterparts of ... fields... However it is then possible to find a frame(s) in which these vectors are mutually parallel, so that the Poynting vector vanishes" (the discussion of these issues can be found in [1]); "when we speak about 'propagation of information', we do not speak strictly about propagation of electromagnetic field in the general sense: the question about the carrier of information ..still remains open"; "there is ... a widespread prejudice that non-inertial frames cannot be used in or they contradict to the special theory of relativity, but this is nothing more than a prejudice" etc. Are many experts familiar with them? Hopefully, people would read his recently published book [2] where these questions from the still open field of Relativistic Physics in Arbitrary Reference Frame have been discussed in detail. Apart, a careful analysis of the Liénard-Wiechert solution has been given in the works by Prof. Mitskievich.

The next paper is by M. Socolovsky from the Universidad Nacional Autónoma de México. He proves the existence of the charge conjugation operator (and, hence, the antiparticle waves) in the nonrelativistic quantum mechanics. The presentation of the basics of the Galilean group, and the corresponding Lagrangian formulation for the Pauli equation are very useful to students. I would like to mention a fact that the interest in the Galilean symmetries has grown recently [3]. The didactic presentation by M. Napsuciale and M.G. Carillo-Ruiz continues the volume. It is dedicated to the study of the Poincare group in d =3+1 and d = 2 + 1 dimensions, as well as the inversion operators C,P and T. In this connection, I recommend the classical books [4], and some of the papers of mine [5].

A theoretical investigation of the neutrino processes is a very important task, including the analysis within extensions of the Standard Model. Prof. Gutiérrez with pupils discusses it in the LRSM (the left-right symmetric model). We decided to include two of his papers, which serve, in fact, as basis for the Theses of his pupils F. Ramí rez-Sánchez and F. Péerez Vargas. The significant result is such that "the spectrum of energy of the electrons for [the beta-decay of tritium] is not affected by the left-right asymmetry parameter". It should be noted that such calculations are necessary in view of the fact that the neutrino oscillations [6] are not described in the Standard Model (the double beta decay, which has been recently claimed to be discovered, as well [7]). The second paper is very useful, indeed, because it presents the basic formalism of the Left-Right Symmetric Model and asserts that the number of visible species of leptons is three.

The Categorical Relativity of Prof. Oziewicz's is the result of his long-standing arguments, "Two Einstein's postulates have nothing to do with the Lorentz group invariance"...Ridiculous? Some people allege that this is true. More rarely in one's opinion would be the author's allegation that "the electromagnetic field is observer-independent" and that the proper time is not unique. The next paper is the one by Prof. Keller. He continues with his research based on the postulates that are given in the book [8], namely "the laws of physics are invariant under the 5D-Poincaré group which includes 5D-Lorentz transformations". The theories in five dimensions have been considered by many authors since the original works by Kaluca, Klein, Dirac (see ref. [9]), Rumer, Kadyshevsky, Greiner etc.

The Hamiltonization of arbitrary ordinary differential equations is an important issue. I prefer, of course, a set of the relativistic equations [10]. R. Alvarado Flores generalizes the Hojman framework which is much more general than that proposed earlier (including assessment from the mathematical viewpoint). The Pérez paper comes up next in our special issue. It is fully mathematical. It is a survey on the meaning of symmetry for a topologist. The J. Martńez Ortiz paper is also a mathematical one. It is related to his PhD Thesis defended recently in St. Petersburg (Russia). Multidisciplinary papers by H. Rosu, J.P. Treviño et al. and A. Enciso Muñoz finish up the special issue. I only wanted to mention that the wavelet transform theory (used in the Rosu papers) found its applications in many areas, including the electromagnetic theory [11]. I am sorry to say that the latter papers are rather of technical interest than of educational one, while the aim of the Workshop was to attract young students to work in mathematical physics.

Finally, I want to thank all participants (particularly outside of Zacatecas) for having come here and presented their thoughtful pieces of research. Next, I apologise for not being able to cite all relevant papers of these (and other) auhors in this Editorial Introduction.

The Workshop has been supported by the PROMEP (SEP, México), Secretarí a Académica de la UAZ (Dr. H. Rene Vega; I believe that participants will remember his inauguration talk - it was published in the UAZ periodicals), CIP UAZ (the Coordinador Mtro. Édgar Hurtado Hernández) and UAF UAZ (the Director Fis. A. Beltrán Mendosa; Cuerpo Académico de Partí culas, Campos y Astrofí sica, Drs. A.A. Espinoza Garrido, A.E. Chubykalo, A. Gutierrez, J. Martinez). We extend our special thanks to our Publisher, our authors and our friends.


  1. Purcell E.M. Electricity and Magnetism, Berkeley Physics Course. - McGraw-Hill. - 1984.
  2. Mitskievich N.V. Relativistic Physics in Arbitrary Reference Frames. - New York: Nova Science Pubs.
    - 2005.
  3. Lévy-Leblond J.M. // Commun.Math.Phys. - 1967. - V. 6. - P. 286.
  4. Kapuscik E. // Acta Phys.Polon. - 1985. - V. B16. - P. 937.
    ibid. // - 1986. - V. 17. - P. 569.
    Communications JINR-P2-10677. - 1977.
    Greenberger D.M. // Phys.Rev.Lett. - 2001. - V. 87. - P. 100405.
    A. van Oosten // Apeiron. - 2006. - N 4. among others.
  5. Gelfand I.M., Minlos R.A. and Shapiro Z.Ya. Representations of the Rotation and Lorentz Groups and Their Applications. - Pergamon Press. - 1963.
    Wigner E. Group Theoretical Concepts and Methods in Elementary Particle Physics. Lectures of the Istanbul School of Theoretical Physics, ed. F. Gürsey. - Gordon and Breach. - 1962.
    Novozhilov Yu. Introduction to Elementary Particle Theory. - Pergamon Press. - 1975.
  6. Dvoeglazov V.V. // Int.J.Theor.Phys. - 1995. - V. 34. - P. 2467.
    // Hadronic J.Suppl. - 1995. - V. 10. - P. 349.
    // Nuovo Cim. - 1996. - V. B111. - P. 483.
    // Fizika - 1997. - V. B6. - P. 111.
    // Hadronic J. - 1997. - V. 20. - P. 435.
    // Acta Phys.Polon. - 1998. - V. B29. - P. 619.
    see also Faustov R.N. Preprint ITF-71-117P. - 1971. among others.
  7. Pontecorvo B. // Zh.E.T.F. - 1958. - V. 34. - P. 247.
    // Phys.Lett. - 1968. - V. B26. - P. 630.
    Bilenky S.M. and Pontecorvo B. // Sov.J.Nucl.Phys. - 1983. - V. 38. - P. 248.
    Bilenky S.M. // Phys.Usp. - 2003. - V. 46. - P. 1137.
    // Phys. Scripta - 2005. - V. T121. - P. 17. among others.
  8. Klapdor-Kleingrothaus H.V. // Part.Nucl.Lett. - 2002. - V. 110. - P. 57.
    // Int.J.Mod.Phys. - 2003. - V. A18. - P. 4113.
    // Nucl.Phys.Proc.Suppl. - 2005. - V. 143. - P. 229. among others.
  9. Keller J. Theory of the Electron. - Kluwer. - 2002.
  10. Dirac P.A.M.J. // J.Math.Phys. - 1963. - V. 4. - P. 901.
  11. Weaver D.L., Hammer C.L. and Good R.H. // Phys.Rev. - 1964. - V. B135. - P. 241.
    Mathews P.M. // ibid. - 1966. - V. 143. - P. 978.
    Williams S.A., Draayer J.P., and Weber T.A. // ibid. - 1966. - V. 152. - P. 1207. and references therein.
  12. Kaiser G. A Friendly Guide to Wavelets: Basic Wavelet Analysis, Physical Wavelets. - Birkhauser. - 1994.
V.V. Dvoeglazov
The Editor
Universidad de Zacatecas
Zacatecas, México
May 2006.

Back to contents

DDFHDJG uggs cheap

DDFJDJG uggs on sale

DDFFKFG cheap uggs

DDFDGDG ugg boots clearance

DDGDGDG cheap ugg boots

DLFDKDG ugg boots christmas

DFSLDDF uggs clearance

SKJDSFG christmas uggs

SKJDSFG christmas uggs boots

SKJDSFG christmas ugg boots


HAPPY NEW YEAR $99.99 uggs clearance
HAPPY NEW YEAR $99.99 uggs boots
HAPPY NEW YEAR $99.99 ugg boots on clearance
HAPPY NEW YEAR $99.99 cheap ugg boots
HAPPY NEW YEAR $99.99 ugg boots clearance
HAPPY NEW YEAR $99.99 cheap ugg boots sale
HAPPY NEW YEAR $99.99 ugg boots cheap

JECCISCADFDF cheap ugg boots for sale

DFDSFDSGFDGG cheap uggs boots

FDSFSFDFDSFD sale ugg boots

DFDFDFDFDFFF uggs on sale cheap

KJDFKFKDJFJF ugg boots sales

FDFDFDFDFDFF cheap uggs boots on sale

DFDFDFDFGHGH cheap ugg boots

CVCVCVCVCVCV cheap ugg boots sale

DSDSDFDFRTHH cheap uggs for sale

FGGFHGJHJKHK uggs on sale

HKHGHDXHFDFG uggs boots on sale

DFDFDFDFDFFD ugg boots on sale


Merry Christmas - 60%OFF ugg boots sale uk,cheap uggs boots on sale - United Kingdom
Happy New Year cheap ugg boots -
Happy New Year ugg boots on sale -
Happy New Year cheap ugg boots uk -
Happy New Year fake ugg boots on sale -
Happy New Year uggs boots uk -
Happy New Year ugg boots sale uk -
Happy New Year -


FGFGFGFGF Cheap UGG Boots UK Sale,Discount UGG Boots On Sale UGGS Online -

GFGFGFGFG cheap ugg boots

EWRETRETT fake ugg boots uk

DFFDFDFFF ugg boots sale uk

FGHJHKJKK discount uggs boots uk

GHGHHHHKJ cheap ugg boots uk

FDDFDFDFG ugg boots sale

GFFGFGFHF cheap ugg boots uk

FGFGFGFHG cheap ugg boots uk sale

FGFGFGHGH cheap ugg boots uk fake

DFFGFGFGG cheap ugg boots uk outlet

FGGFGFGFH cheap ugg boots

DFGFGFGHG ugg boots


SGDFG cheap ugg boots sale
GHHGH ugg boots on sale
FGFGV cheap uggs on sale
DFDFF uggs for cheap

jack wills sale
jack wills outlet
jack wills outlet uk
jack wills cheap

cheap ugg boots
cheap ugg boots
uggs clearance
ugg boots clearance
cheap ugg boots sale
cheap ugg boots sale
ugg boots clearance
cheap ugg boots
cheap ugg boots for sale
cheap ugg boots on sale
ugg boots on sale
cheap ugg boots
UGG BLOG SFHKJFS cheap ugg boots for sale -
UGGS BLOG DSKFJD cheap ugg boots sale -
UGG BLOG DGFGFFF cheap uggs on sale -
UGG BLOG DFDFDFG cheap ugg boots -
UGG BLOG DGFGFGF ugg boots on sale -
UGG BLOG FGFGDFD sale ugg boots -
UGG BLOG FDDGGGG uggs cheap -
dfdfdfds cheap ugg boots for sale -
fgfgvghg cheap ugg boots on sale -
gfgfgfgf cheap uggs sale -
fgfggggh cheap uggs on sale -
ghghghgh cheap uggs for sale -
SDAKFJF cheap ugg boots -
DSKDSDJS cheap ugg boots sale -
SFDFDFFF cheap uggs for sale -
SDSDSDSD ugg boots clearance -
SDSFDFDF uggs clearance -

NFLNIKEPRICE45.99 Tim Tebow Nike Elite Jersey Green 15 New York Jets Jersey


NFLNIKEPRICE45.99 Tim Tebow Jersey


NFLNIKEPRICE45.99 Tim Tebow Jersey


NFLNIKEPRICE45.99 Tim Tebow Jersey


NFLNIKEPRICE45.99 Tim Tebow Jersey


NFLNIKEPRICE45.99 Tim Tebow White Nike NFL Jerseys


NFLNIKEPRICE45.99 Tim Tebow Green Nike NFL Jerseys


NFLNIKEPRICE45.99 Robert Griffin III Nike Elite Jersey Red 10 Washington Redskins Jersey


NFLNIKEPRICE45.99 Peyton Manning Nike Elite Jersey


NFLNIKEPRICE45.99 Peyton Manning Jersey


NFLNIKEPRICE45.99 Peyton Manning Jersey


NFLNIKEPRICE45.99 Peyton Manning Jersey


NFLNIKEPRICE45.99 Peyton Manning Jersey


NFLNIKEPRICE45.99 Peyton Manning White Nike NFL Jerseys


NFLNIKEPRICE45.99 Peyton Manning Orange Women Nike NFL Jerseys


NFLNIKEPRICE45.99 Peyton Manning Orange Nike NFL Jerseys


NFLNIKEPRICE45.99 nike nfl jerseys