Gennadi Sardanashvily

<h2 id="biography">Biography</h2>
Gennadi Sardanashvily graduated from <a href="/facts/Moscow_State_University/xHPG4oau">Moscow State University</a> (MSU) in 1973, he was a Ph.D. student of the Department of Theoretical Physics (<a href="/facts/Moscow_State_University/xHPG4oau">MSU</a>) in 1973–76, where he held a position in 1976.
He attained his Ph.D. degree in physics and mathematics from <a href="/facts/Moscow_State_University/xHPG4oau">MSU</a>, in 1980, with <a href="/facts/Dmitri_Ivanenko/EbgISrnl">Dmitri Ivanenko</a> as his supervisor, and his D.Sc. degree in physics and mathematics from <a href="/facts/Moscow_State_University/xHPG4oau">MSU</a>, in 1998.
Gennadi Sardanashvily was the founder and Managing Editor (2003 - 2013) of the <a href="/facts/International_Journal_of_Geometric_Methods_in_Modern_Physics/aG9TbccV">International Journal of Geometric Methods in Modern Physics</a> (IJGMMP).
He was a member of Lepage Research Institute (Slovakia).

<h2 id="research-area">Research area</h2>
Gennadi Sardanashvily research area is geometric method in <a href="/facts/Classical_mechanics/ykG8upsN">classical</a> and <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> and <a href="/facts/Classical_field_theory/7HuKY1qu">field theory</a>, <a href="/facts/Gravitation/bqAN7DdQ">gravitation theory</a>. His main achievement is geometric formulation of <a href="/facts/Classical_field_theory/7HuKY1qu">classical field theory</a> and <a href="/facts/Non-autonomous_mechanics/cdz9tvsY">non-autonomous mechanics</a> including:

<ul><li><a href="/facts/Gauge_gravitation_theory/wwRu94cD">gauge gravitation theory</a>, where gravity is treated as a <a href="/facts/Higgs_field_(classical)/2mrn1nDu">classical Higgs field</a> associated to a reduced Lorentz structure on a world manifold<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a></li>
<li>geometric formulation of <a href="/facts/Classical_field_theory/7HuKY1qu">classical field theory</a><a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> and Lagrangian <a href="/facts/BRST_formalism/BdNA0oDH">BRST</a> theory<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> where classical fields are represented by sections of <a href="/facts/Fiber_bundle/SJ7Ek6cI">fiber bundles</a> and their dynamics is described in terms of <a href="/facts/Jet_bundle/7RHyhv07">jet manifolds</a> and the <a href="/facts/Variational_bicomplex/dVImNVSP">variational bicomplex</a> (<a href="/facts/Covariant_classical_field_theory/dYegRrqf">covariant classical field theory</a>)</li>
<li><a href="/facts/Covariant_Hamiltonian_field_theory/aWRhRJF0">covariant (polysymplectic) Hamiltonian field theory</a>, where momenta correspond to derivatives of fields with respect to all world coordinates<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a></li>
<li>the <a href="/facts/Noether%27s_second_theorem/RHInV7cV">second Noether theorem</a> in a very general setting of <a href="/facts/Noether_identities/Dy4EB4VN">reducible degenerate</a> Grassmann-graded <a href="/facts/Lagrangian_system/3w7eSwYg">Lagrangian systems</a> on an arbitrary manifold<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a></li>
<li>geometric formulation of classical<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> and quantum<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> <a href="/facts/Non-autonomous_mechanics/cdz9tvsY">non-autonomous mechanics</a> on <a href="/facts/Fiber_bundle/SJ7Ek6cI">fiber bundles</a> over 
 
 
 
 
 R
 
 
 
 {\displaystyle \mathbb {R} }
 
</li>
<li>generalization of the Liouville–Arnold, Nekhoroshev and Mishchenko–Fomenko theorems on <a href="/facts/Integrable_system/Crgzjw6G">completely</a> and <a href="/facts/Integrable_system/Crgzjw6G">partially integrable</a> and <a href="/facts/Superintegrable_Hamiltonian_system/XnpdUfJY">superintegrable Hamiltonian systems</a> to the case of non-compact invariant submanifolds<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a></li>
<li>cohomology of the <a href="/facts/Variational_bicomplex/dVImNVSP">variational bicomplex</a> of <a href="/facts/Graded_manifold/cr99oc5R">graded differential forms</a> of finite jet order on an infinite order jet manifold.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a></li></ul>
Gennadi Sardanashvily has published more than 400 scientific works, including 28 books.

<h2 id="selected-monographs">Selected monographs</h2>
<ul><li>Sardanashvily, G.; Zakharov, O. (1992), Gauge Gravitation Theory, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-02-0799-9.</li></ul>
<ul><li>Sardanashvily, G. (1993), Gauge Theory on Jet Manifolds, Hadronic Press, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-911767-60-6.</li></ul>
<ul><li>Sardanashvily, G. (1995), Generalized Hamiltonian Formalism for Field Theory, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-02-2045-6.</li></ul>
<ul><li>Giachetta, G.; Mangiarotti, L.; Sardanashvily, G. (1997), New Lagrangian and Hamiltonian Methods in Field Theory, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-02-1587-8.</li></ul>
<ul><li>Mangiarotti, L.; Sardanashvily, G. (1998), Gauge Mechanics, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-02-3603-4.</li></ul>
<ul><li>Mangiarotti, L.; Sardanashvily, G. (2000), Connections in Classical and Quantum Field Theory, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-02-2013-8.</li></ul>
<ul><li>Giachetta, G.; Mangiarotti, L.; Sardanashvily, G. (2005), Geometric and Algebraic Topological Methods in Quantum Mechanics, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 981-256-129-3.</li></ul>
<ul><li>Giachetta, G.; Mangiarotti, L.; Sardanashvily, G. (2009), Advanced Classical Field Theory, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-981-283-895-7.</li></ul>
<ul><li>Giachetta, G.; Mangiarotti, L.; Sardanashvily, G. (2011), Geometric formulation of classical and quantum mechanics, World Scientific, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-981-4313-72-8.</li></ul>
<ul><li>Sardanashvily, G. (2012), Lectures on Differential Geometry of Modules and Rings. Application to Quantum Theory, Lambert Academic Publishing, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-659-23806-2.</li></ul>
<ul><li>Sardanashvily, G. (2013), Advanced Differential Geometry for Theoreticians. Fiber bundles, jet manifolds and Lagrangian theory, Lambert Academic Publishing, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-659-37815-7.</li></ul>
<ul><li>Sardanashvily, G. (2015), Handbook of Integrable Hamiltonian Systems, URSS, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-5-396-00687-4.</li></ul>
<ul><li>Sardanashvily, G. (2016), Noether's Theorems. Applications in Mechanics and Field Theory, Springer, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-94-6239-171-0.</li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://istina.msu.ru/profile/sardanashvily/">Personal page at Moscow State University</a> (in Russian)</li>
<li><a href="http://gnsardan.appfarm.ru/">Gennadi Sardanashvily's personal site</a></li>
<li><a href="https://sites.google.com/site/sardanashvily/home">Gennadi Sardanashvily's site at Google</a></li>
<li><a href="https://web.archive.org/web/20160304074329/http://gnsardan.appfarm.ru/sard-biography-engl.pdf">Scientific Biography</a></li>
<li><a href="https://www.researchgate.net/profile/G_Sardanashvily">List of publications at ResearchGate</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">"Obituary of Professor Gennadi Sardanashvily". International Journal of Geometric Methods in Modern Physics. <a href="http://www.worldscientific.com/page/ijgmmp/Gennadi-Sardanashvily" target="_blank">http://www.worldscientific.com/page/ijgmmp/Gennadi-Sardanashvily</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">D. Ivanenko, G. Sardanashvily, The gauge treatment of gravity, Physics Reports 94 (1983) 1–45. <a href="/wiki/Dmitri_Ivanenko" target="_blank">/wiki/Dmitri_Ivanenko</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">G. Giachetta, L. Mangiarotti, G. Sardanashvily, Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology, Commun. Math. Phys. 295 (2005) 103–128; arXiv:hep-th/0407185. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">D. Bashkirov, G. Giachetta, L. Mangiarotti, G. Sardanashvily, The KT-BRST complex of a degenerate Lagrangian theory, Lett. Math. Phys. 83 (2008) 237–252; arXiv:math-ph/0702097. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">G. Giachetta, L. Mangiarotti, G. Sardanashvily, Covariant Hamiltonian equations for field theory, J. Phys. A 32 (1999) 6629–6642; arXiv:hep-th/9904062. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">G. Giachetta, L. Mangiarotti, G. Sardanashvily, On the notion of gauge symmetries of generic Lagrangian field theory, J. Math. Phys. 50 (2009) 012903; arXiv:0807.3003. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">G. Sardanashvily, Hamiltonian time-dependent mechanics, J. Math. Phys. 39 (1998) 2714–2729. <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">L.Mangiarotti, G. Sardanashvily, Quantum mechanics with respect to different reference frames, J. Math. Phys. 48 (2007) 082104; arXiv:quant-ph/0703266. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">E. Fiorani, G. Sardanashvily, Global action-angle coordinates for completely integrable systems with non-compact invariant submanifolds, J. Math. Phys. 48 (2007) 032901; arXiv:math/0610790. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">G. Sardanashvily, Graded infinite order jet manifolds, Int. J. Geom. Methods Mod. Phys. 4 (2007) 1335–1362; arXiv:0708.2434 <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
</ol>

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Gennadi Sardanashvily