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New Lagrangian and Hamiltonian Methods in Field Theory

- G. Giachetta, L. Mangiarotti, G. Sardanashvily
- Mathematics
- 19 December 1997

This work incorporates three modern aspects of mathematical physics: the jet methods in differntial geometry, the Lagrangian formalism on jet manifolds and the multimomentum approach to the… Expand

The variational bicomplex on graded manifolds and its cohomology

- G. Sardanashvily
- Mathematics
- 26 April 2005

Lagrangian formalism on graded manifolds is phrased in terms of the Grassmann-graded variational bicomplex, generalizing the familiar variational bicomplex for even Lagrangian systems on fiber… Expand

What is geometry in quantum theory

- G. Sardanashvily, G. Giachetta
- Physics, Mathematics
- 13 January 2004

In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.

On the geometry of spontaneous symmetry breaking

- G. Sardanashvily
- Physics
- 1 April 1992

Given a principal bundle P→X with a structure group G and an associated Higgs bundle Σ with a standard fiber G/H, the case of a matter bundle E whose standard fiber admits action only of an exact… Expand

The gauge treatment of gravity

- D. Ivanenko, G. Sardanashvily
- Physics
- 1983

Abstract The gauge gravitation theory, in spite of twenty five years of its history, still remains the single gap in the excellent gauge picture of fundamental interactions. The main disputable point… Expand

Advanced Classical Field Theory

- G. Giachetta, L. Mangiarotti, G. Sardanashvily
- Mathematics
- 4 May 2009

Differential Calculus on Fiber Bundles Lagrangian Theory on Fiber Bundles Covariant Hamiltonian Field Theory Grassmann-Graded Lagrangian Theory Lagrangian BRST Theory Gauge Theory on Principal Fiber… Expand

Connections in Classical and Quantum Field Theory

- L. Mangiarotti, G. Sardanashvily
- Mathematics
- 15 September 2000

Elementary gauge theory geometry of fiber bundles geometric gauge theory gravitation topological invariants in field theory jet bundle formalism Hamiltonian formalism in field theory… Expand

Geometric And Algebraic Topological Methods In Quantum Mechanics

- G. Giachetta, L. Mangiarotti, G. Sardanashvily
- Mathematics
- 28 January 2005

Commutative Geometry Classical Hamiltonian Systems Algebraic Quantization Geometry of Algebraic Quantization Geometric Quantization Supergeometry Deformation Quantization Non-Commutative Geometry… Expand

Hamiltonian time-dependent mechanics

- G. Sardanashvily
- Mathematics
- 23 October 1998

The usual formulation of time-dependent mechanics implies a given splitting Y=R×M of an event space Y. This splitting, however, is broken by any time-dependent transformation, including… Expand

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