Gauge complex field theory.
Gauge independent formulation of dynamics of charged extended objects
Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields
Gauge symmetry and Howe duality in 4D conformal field theory models.
Gauge theories on deformed spaces.
Gauge theory and calibrated geometry. I.
Generalized Chern-Simons theory and skein relations in arbitrary dimensions
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Generalized nonanalytic expansions, -symmetry and large-order formulas for odd anharmonic oscillators.
Generalized Potts-models and their relevance for gauge theories.
Generalized SU (2) theta functions.
Geometric modular action and transformation groups
Geometric physics.
Geometrical and topological foundations of theoretical physics: from gauge theories to string program.
Geometrical background for the unified field theories : the Einstein-Cartan theory over a principal fibre bundle
Gerbes and homotopy quantum field theories.
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.
Global properties of vacuum states in de Sitter space
Global Waves with Non-Positive Energy in General Relativity
2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.The theory of the waves equations has a long history since M. Riesz and J. Hadamard. It is impossible to cite all the important results in the area, but we mention the authors related with our work: J. Leray [34] and Y. Choquet-Bruhat [9] (Cauchy problem), P. Lax and R. Phillips [33] (scattering theory for a compactly supported perturbation), L. H¨ ormander [27] and J-M. Bony [7] (microlocal analysis). In all these domains, V. Petkov has...
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...