2024-04-12T18:26:15Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/507512023-08-26T05:18:00Zcom_20.500.14352_14col_20.500.14352_15
00925njm 22002777a 4500
dc
Castrillón López, Marco
author
Muñoz Masqué, Jaime
author
2007
Let C → M be the bundle of connections of a principal G-bundle P → M over a pseudo-Riemannian manifold (M,g) of signature (n+, n−) and let E → M be the associated bundle with P under a linear representation of G on a finite-dimensional vector space. For an arbitrary Lie group
G, the O(n+,n-) × G-invariant quadratic Lagrangians on J1(C ×M E) are characterized. In particular, for a simple Lie group the Yang–Mills and Yang–Mills–Higgs Lagrangians are characterized, up to an scalar factor, to be the only O(n+, n−) × G-invariant quadratic Lagrangians. These results are also analyzed on several examples of interest in gauge theory.
M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207.
D. Betounes, The geometry of gauge-particle field interaction: a generalization of Utiyama’s theorem, J. Geom. Phys. 6 (1989), 107–125.
D. Bleecker, Gauge Theory and Variational Principles, Addison-Wesley Publishing Company, Inc., Reading, MA, 1981.
D. J. Eck, Gauge-natural bundles and generalized gauge theories, Mem. Amer. Math. Soc. 33 (1981), no. 247.
D. S. Freed, Classical Chern–Simons theory. I , Adv. Math. 113 (1995), no. 2, 237–303.
P. L. García, Connections and 1-jet bundles, Rend. Sem. Mat. Univ. Padova 47 (1972), 227–242.
P. L. García, Gauge algebras, curvature and symplectic structure, J. Differential Geom. 12 (1977), 209–227.
R. Goodman, N.R. Wallach, Representations and invariants of the classical groups, Encyclopedia of Mathematics and its Applications 68, Cambridge University Press, Cambridge,1998.
V. Guillemin, S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, Cambridge, UK, 1983.
T. Hagiwara, A non-abelian Born–Infeld Lagrangian, J. Phys. A: Math. Gen. 14(1981), 3059–3065.
S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, JohnWiley & Sons,Inc. (Interscience Division), New York, Volume I, 1963; Volume II, 1969.
S. Kuwata, Born–Infeld Lagrangian using Cayley–Dickson algebras, Internat. J. Modern Phys. A 19 (2004), no. 10, 1525–1548.
A. Onishchik, Lectures on Real Semisimple Lie Algebras and their Representations, European Mathematical Society,Zürich, 2004.
R. Utiyama, Invariant Theoretical Interpretation of Interaction, Phys. Rev. 101(1956), 1597–1607.
A. Zee, Quantum Field Theory in a Nutshell , Princeton University Press, New Jersey,2003.
1424-0637
10.1007/s00023-006-0305-5
https://hdl.handle.net/20.500.14352/50751
http://link.springer.com/content/pdf/10.1007%2Fs00023-006-0305-5.pdf
http://link.springer.com
Gauge-Invariant Characterization of Yang–Mills–Higgs Equations