zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Yang-Mills fields and gauge gravity on generalized Lagrange and Finsler spaces. (English) Zbl 0842.53020
In the framework of the theory of linear connections in vector bundles (with semisimple structural groups) on generalized Lagrange spaces, a geometrical approach to interactions of Yang-Mills fields on spaces with local anisotropy is formulated. The geometrical formalism is extended in a manner including theories with nonsemisimple groups which permit a unique fiber bundle treatment for both locally anisotropic Yang-Mills and gravitational interactions. One of the most important results of the paper is formulated as a theorem stating that almost Hermitian Lagrange gravity -- described in {\it R. Miron} and {\it M. Anastasiei} [The geometry of Lagrange spaces: theory and applications. Fundamental Theories of Physics, 59, Dordrecht: Kluwer Academic Publishers (1994; Zbl 0831.53001)], is equivalent to a gaugelike theory in the bundle of affine adapted frames on generalized Lagrange spaces.

53C07Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
81T13Yang-Mills and other gauge theories
83C47Methods of quantum field theory in general relativity
53Z05Applications of differential geometry to physics
Full Text: DOI
[1] Aldovandi, R., and Stedile, E. (1984).International Journal of Theoretical Physics,23, 301. · Zbl 0541.53056 · doi:10.1007/BF02114511
[2] Asanov, G. S., and Ponomarenko, S. F. (1989).Finder Bundles on Space-Time. Associated Gauge Fields and Connections, Stiinta, Chisinau, Moldova [in Russian]. · Zbl 0708.53001
[3] Bishop, R. L., and Crittenden, R. L. (1965).Geometry of Manifolds, Academic Press, New York. · Zbl 0146.43304
[4] Kadic, A., and Edelen, D. (1983).A Gauge Theory of Dislocations and Disclinations, Springer-Verlag, Berlin. · Zbl 0523.73089
[5] Luehr, C. P., and Rosenbaum, M. (1980).Journal of Mathematical Physics,21, 1432. · Zbl 0453.22011 · doi:10.1063/1.524569
[6] Matsumoto, M. (1986).Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press. · Zbl 0594.53001
[7] Miron, R. (1985). A Lagrangian theory of gravity, Preprint 84, University of Timisoara, Romania. · Zbl 0574.53050
[8] Miron, R., and Anastasiei, M. (1993).The Geometry of Lagrange Spaces: Theory and Applications, Kluwer, Dordrecht. · Zbl 0831.53001
[9] Miron, R., and Kawaguchi, T. (1991).International Journal of Theoretical Physics,30, 1521. · Zbl 0746.53060 · doi:10.1007/BF00675616
[10] Ponomarev, V. N., Barvinsky, A. O., and Obukhov, Yu. N. (1985).Geometrodynamical Methods and Gauge Approach to Gravity Theory, Energoatomizdat, Moscow [in Russian].
[11] Popov, D. A. (1975).Theoretical and Mathematical Physics,24, 347 [in Russian]. · Zbl 0412.53014 · doi:10.1007/BF01029874
[12] Popov, D. A., and Daikhin, L. I. (1975).Doklady Academy of Sciences USSR,225, 790 [in Russian].
[13] Popov, D. A., and Daikhin, L. I. (1976).Soviet Physics Doklady,20, 818.
[14] Tseytlin, A. A. (1982).Physical Review D,26, 3327. · doi:10.1103/PhysRevD.26.3327
[15] Vacaru, S. I. (1987).Vestnik Moskow University, Physics and Astronomy,28, 5 [in Russian].
[16] Vacaru, S. (1991). InMethods of Quantum Field Theory in Condensed Matter Physics, P. I. Hadji, ed., Stiinta, Chisinau, Moldova, p. 98 [in Russian].
[17] Vacaru, S. I. (1993).Buletinul Academiei de Stiinte a Republicii Moldova, Fizica si Tehnica,3, 17.
[18] Vacaru, S. I. (1994).Romanian Journal of Physics,39, 37.
[19] Vacaru, S. I. (1995a). Statistical distribution functions in generalized Lagrange spaces, in preparation.
[20] Vacaru, S. I. (1995b). Spinor structures and nonlinear connections in vector bundles, generalized Lagrange and Finsler spaces,Journal of Mathematical Physics, to appear.
[21] Vacaru, S. I., and Ostaf, S. V. (1993).Buletinul Academiei de Suinte a Republicii Moldova, Fizica si Tehnica,3, 5.
[22] Vacaru, S. I., Ostaf, S. V., Goncharenko, Yu. A., and Doina, A. V. (1994).Buletinul Academiei de Stiinte a Republicii Moldova, Fizica si Tehnica,3, 42.
[23] Vlasov, A. A. (1966).Statistical Distribution Functions, Nauka, Moscow [in Russian].
[24] Walner, R. P. (1985).General Relativity and Gravitation,17, 1081. · Zbl 0567.53052 · doi:10.1007/BF00774210