Related papers: Non-Linear Algebra and Bogolubov's Recursion
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yield a new formula for the number of NATs. We also obtain…
In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions…
Puts forward a complete scenario for interpreting nonlinear field theories highlighting the role played by gravitational self--energy in enabling a consistent revival of the Schroedinger approach to unifying micro and macro physics.
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis…
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic…
Based on a recent classification of subalgebras of the symmetry algebra of the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation into ordinary differential equations are obtained. Large classes of group-invariant…
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify…
Relativistic quantum field theories for complex scalar and Dirac fields are investigated in non-equilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two…
Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…
We review some applications of Gr\"obner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We obtain a parametric normal form for any non-degenerate perturbation of the generalized saddle-node case of Bogdanov--Takens singularity. Explicit formulas are derived and greatly simplified for an efficient implementation in any computer…
All coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by $\{\aa,\ap,\am,\bb\}$. Quantum oscillator algebras are derived from these bialgebras by using the…
The Girsanov transform and Kolmogorov equations are two useful methods for studying SPDEs. It is shown that, under suitable conditions, the series expansion obtained from the Girsanov transform coincides with the one generated by an…
Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…
We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…