The symmetries of generic 2D dilaton models of gravity with (and without) matter are studied in some detail. It is shown that δ2, one of the symmetries of the matterless models, can be generalized to the case where matter fields of any kind are present. The general (classical) solution for some of these models, in particular those coupled to chiral matter, which generalizes the Vaidya solution ...

We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that pseudogroup these has exactly two connected components. That is, admits single independent discrete symmetry, which can be chosen alternating sign dependent variable. introduce notion pseudo-discrete elements Lie group show sp...

We review a notion of completeness in QFT arising from the analysis basic properties set operator algebras attached to regions. In words, this asserts that physical observable produced by local degrees freedom are maximal ones compatible with causality. elaborate on equivalent statements principle such as non-existence generalized symmetries and uniqueness net algebras. clarify for non-complete...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area pr...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area pr...

I discuss and extend several results concerning the cancellation of discrete gauge anomalies. I show how heavy fermions do not decouple in the presence of discrete gauge anomalies. As a consequence, in general, cancellation of discrete gauge anomalies cannot be described merely in terms of low energy operators involving only the light fermions. I also discuss cancellation of discrete gauge anom...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contents a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserv...

Abstract We consider integrability structures of the generalized Hunter–Saxton equation. obtain Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra higher symmetries, prove existence infinite number cosymmetries order. Further, we give examples employing order to constructing exact...