• Publications
  • Influence
New Lagrangian and Hamiltonian Methods in Field Theory
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 theExpand
The variational bicomplex on graded manifolds and its cohomology
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 fiberExpand
What is geometry in quantum theory
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
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 exactExpand
The gauge treatment of gravity
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 pointExpand
Advanced Classical Field Theory
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 FiberExpand
Connections in Classical and Quantum Field Theory
Elementary gauge theory geometry of fiber bundles geometric gauge theory gravitation topological invariants in field theory jet bundle formalism Hamiltonian formalism in field theoryExpand
Geometric And Algebraic Topological Methods In Quantum Mechanics
Commutative Geometry Classical Hamiltonian Systems Algebraic Quantization Geometry of Algebraic Quantization Geometric Quantization Supergeometry Deformation Quantization Non-Commutative GeometryExpand
Hamiltonian time-dependent mechanics
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, includingExpand