The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
The essential spectrum of relativistic multi-particle operators
The essential spectrum of relativistic one-electron ions in the Jansen-Hess model.
The evolution of the Dirac field in cuved space-times.
The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks
Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...
The exocenter and type decomposition of a generalized pseudoeffect algebra
We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...
The fermion number processes as a functional central limit of quantum hamiltonian models
The Feynman integral and Feynman's operational calculus: a heuristic and mathematical introduction
The Foldy-Wouthuysen transformation in the two-particle case
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The form factor program: a review and new results - the nested off-shell Bethe ansatz.
The Fourier transform on quantum Euclidean space.
The Frobenius theorem on -dimensional quantum hyperplane.
The Gap Phenomena of Yang-Mills Fields over the Complete Manifold.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The generalized Lichnerowicz formula and analysis of Dirac operators.
The geometric quantization of the moduli space of Riemann surfaces with even spin structure.
The geometry of Brownian surfaces.
The geometry of Calogero-Moser systems
We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the -th power of the elliptic curve, where is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...