Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. The introduction of the equivalence being consistent with the mathematical definition is possible only in theories constructed on nonstandard number spaces by taking the experimental errors as infinitesimal numbers of the non-standard spaces. Following the idea for the equivalence (the phys...

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...

We show that biholomorphic automorphisms of a real analytic hypersurface in I C can be considered as (pointwise) Lie symmetries of a holomorphic completely overdetermined involutive second order PDE system defining its Segre family. Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of such a system and give a new proof of some well known results of CR...

Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

An infinite-dimensional algebra of all infinitesimal transformations of solutions to the self-dual Yang-Mills equations is described. As subalgebras it contains the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations.

We fully develop the concept of causal symmetry introduced in [19]. A causal symmetry is a transformation of a Lorentzian manifold (V, g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual composition operation but a submonoid of the diffeomorphism group of V . Therefore, the infinitesimal generati...

We fully develop the concept of causal symmetry introduced in [21]. A causal symmetry is a transformation of a Lorentzian manifold (V, g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual composition operation but a submonoid of the diffeomorphism group of V . Therefore, the infinitesimal generati...