Quantum theory of fields and branes,
supersymmetric quantum mechanics,
mathematical aspects of cosmology,
isospectral transformations,
non-Hermitian operators, path integrals.
Main publications:
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra.
By A. A. Andrianov & A. V. Sokolov.
J. Math. Sci. 143, 2707–2722, 2007. [arXiv:0710.5738]
On the stability of thick brane worlds non-minimally coupled to gravity.
By A. A. Andrianov & Luca Vecchi. Phys. Rev. D 77, 044035, 2008. [arXiv:0711.1955]
Dual oscillators and Quantum Pendulums: spectrum and correlators.
By A. A. Andrianov.
Phys. Rev. D 76, 025003, 2007. [hep-th/0703052]
Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians. I. General properties.
A. A. Andrianov, F. Cannata, A. V. Sokolov.
Nucl. Phys. B 773, 107–136, 2007. [math-ph/0610024]
Complex Lagrangians and phantom cosmology.
By A. A. Andrianov, F. Cannata, A. Y. Kamenshchik.
J. Phys. A 39, 9975–9982, 2006. [gr-qc/0604126]
Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians: Puzzles with self-orthogonal states.
By A. V. Sokolov, A. A. Andrianov, F. Cannata. J. Phys. A 39, 10207–10228, 2006. [quant-ph/0602207]
Chiral dynamics from the hadronic string: General formalism.
By A. A. Andrianov, D. Espriu, A. Prats.
Int. J. Mod. Phys. A 21, 3337–3366, 2006. [hep-th/0507212]
Smooth dynamical crossing of the phantom divide line of a scalar field in simple cosmological models.
By Alexander A. Andrianov, Francesco Cannata, Alexander Y. Kamenshchik.
Phys. Rev. D 72, 043531, 2005. [gr-qc/0505087]
Brane world generation by matter and gravity.
By A. A. Andrianov, V. A. Andrianov, P. Giacconi, R. Soldati.
JHEP 0507, 003, 2005. [hep-th/0503115]
Nonlinear supersymmetry in quantum mechanics: Algebraic properties and differential representation.
By A. A. Andrianov & A. V. Sokolov.
Nucl. Phys. B 660, 25–50, 2003. [hep-th/0301062]
