Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 2, Pages 377–389
DOI: https://doi.org/10.4213/tmf6094 (Mi tmf6094) 		 
This article is cited in 16 scientific papers (total in 16 papers)

The relation between the Jacobi morphism and the Hessian in gauge-natural field theories

M. Palese, E. Winterroth

University of Torino
Full-text PDF (492 kB) Citations (16)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf6094
Abstract: We generalize a classic result, due to Goldschmidt and Sternberg, relating the Jacobi morphism and the Hessian for first-order field theories to higher-order gauge-natural field theories. In particular, we define a generalized gauge-natural Jacobi morphism where the variation vector fields are Lie derivatives of sections of the gauge-natural bundle with respect to gauge-natural lifts of infinitesimal principal automorphisms, and we relate it to the Hessian. The Hessian is also very simply related to the generalized Bergmann–Bianchi morphism, whose kernel provides necessary and sufficient conditions for the existence of global canonical superpotentials. We find that the Hamilton equations for the Hamiltonian connection associated with a suitably defined covariant strongly conserved current are satisfied identically and can be interpreted as generalized Bergmann–Bianchi identities and thus characterized in terms of the Hessian vanishing.
Keywords: jet, gauge-natural bundle, second variational derivative, generalized Jacobi morphism.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 2, Pages 1191–1200
DOI: https://doi.org/10.1007/s11232-007-0102-4
Bibliographic databases:
Language: Russian
Citation: M. Palese, E. Winterroth, “The relation between the Jacobi morphism and the Hessian in gauge-natural field theories”, TMF, 152:2 (2007), 377–389; Theoret. and Math. Phys., 152:2 (2007), 1191–1200
Citation in format AMSBIB
\Bibitem{PalWin07}
\by M.~Palese, E.~Winterroth
\paper The~relation between the Jacobi morphism and the Hessian in gauge-natural field theories
\jour TMF
\yr 2007
\vol 152
\issue 2
\pages 377--389
\mathnet{http://mi.mathnet.ru/tmf6094}
\crossref{https://doi.org/10.4213/tmf6094}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2429287}
\zmath{https://zbmath.org/?q=an:1186.70020}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2007TMP...152.1191P}
\elib{https://elibrary.ru/item.asp?id=9541942}
\transl
\jour Theoret. and Math. Phys.
\yr 2007
\vol 152
\issue 2
\pages 1191--1200
\crossref{https://doi.org/10.1007/s11232-007-0102-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000249211500014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548460310}
Linking options:
  • https://www.mathnet.ru/eng/tmf6094
  • https://doi.org/10.4213/tmf6094
  • https://www.mathnet.ru/eng/tmf/v152/i2/p377
    • This publication is cited in the following 16 articles:
    1. Jana Musilová, Pavla Musilová, Olga Rossi, Lecture Notes in Physics, 1033, Calculus of Variations on Fibred Manifolds and Variational Physics, 2025, 1  crossref
    2. Federico Chiaffredo, Lorenzo Fatibene, Marco Ferraris, Emanuele Ricossa, Davide Usseglio, “A variational framework for higher order perturbations”, Int. J. Geom. Methods Mod. Phys., 21:10 (2024)  crossref
    3. Accornero L., Palese M., “Symmetry Transformations of Extremals and Higher Conserved Quantities: Invariant Yang-Mills Connections”, J. Math. Phys., 62:4 (2021), 043504  crossref  mathscinet  isi
    4. Accornero L., Palese M., “The Jacobi Morphism and the Hessian in Higher Order Field Theory; With Applications to a Yang-Mills Theory on a Minkowskian Background”, Int. J. Geom. Methods Mod. Phys., 17:8 (2020), 2050114  crossref  mathscinet  isi
    5. Palese M., Winterroth E., “Higgs Fields Induced By Yang-Mills Type Lagrangians on Gauge-Natural Prolongations of Principal Bundles”, Int. J. Geom. Methods Mod. Phys., 16:3 (2019), 1950049  crossref  mathscinet  isi  scopus
    6. Palese M., Winterroth E., “Topological obstructions in Lagrangian field theories, with an application to 3D Chern–Simons gauge theory”, J. Math. Phys., 58:2 (2017), 023502  crossref  mathscinet  zmath  isi  scopus
    7. Marcella Palese, Olga Rossi, Ekkehart Winterroth, Jana Musilová, “Variational Sequences, Representation Sequences and Applications in Physics”, SIGMA, 12 (2016), 045, 45 pp.  mathnet  crossref
    8. Palese M., Winterroth E., “Classical Higgs Fields on Gauge Gluon Bundles”, Qcd@Work 2016 - International Workshop on Quantum Chromodynamics - Theory and Experiment, Epj Web of Conferences, 129, eds. Bruno G., Chiodini G., Colangelo P., Coriano C., Creanza D., DeFazio F., Nappi E., Spagnolo S., E D P Sciences, 2016, UNSP 00016  crossref  isi  scopus
    9. Palese M., Winterroth E., “Higgs Fields on Spinor Gauge-Natural Bundles”, Xxth International Conference on Integrable Systems and Quantum Symmetries (Isqs-20), Journal of Physics Conference Series, 411, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013, 012025  crossref  isi  scopus
    10. Francaviglia M., Palese M., Winterroth E., “Variationally Equivalent Problems and Variations of Noether Currents”, Int. J. Geom. Methods Mod. Phys., 10:1 (2013), 1220024  crossref  mathscinet  zmath  isi  elib  scopus
    11. Francaviglia M., Palese M., Winterroth E., “Cohomological Obstructions in Locally Variational Field Theories”, Xxist International Conference on Integrable Systems and Quantum Symmetries (Isqs21), Journal of Physics Conference Series, 474, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013  crossref  mathscinet  isi  scopus
    12. Ferraris M., Francaviglia M., Palese M., Winterroth E., “Gauge-Natural Noether Currents and Connection Fields”, Int J Geom Methods Mod Phys, 8:1 (2011), 177–185  crossref  mathscinet  zmath  isi  elib  scopus
    13. M. Palese, E. Winterroth, “A variational perspective on classical Higgs fields in gauge-natural theories”, Theoret. and Math. Phys., 168:1 (2011), 1002–1008  mathnet  crossref  crossref  mathscinet  isi
    14. Palese M., Winterroth E., “Invariant Variational Problems and Cartan Connections on Gauge-Natural Bundles”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 160–165  crossref  adsnasa  isi  scopus
    15. Palese M, Winterroth E, “LAGRANGIAN REDUCTIVE STRUCTURES ON GAUGE-NATURAL BUNDLES”, Reports on Mathematical Physics, 62:2 (2008), 229–239  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Ferraris M, Francaviglia M, Palese M, “CANONICAL CONNECTIONS IN GAUGE-NATURAL FIELD THEORIES”, International Journal of Geometric Methods in Modern Physics, 5:6 (2008), 973–988  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:454
    Full-text PDF :202
    References:47
    First page:2
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025