Related papers: A geometric approach to the generalized Noether th…
The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer's trajectory, has recently been developped. It naturally solves some…
A general approach to find out exact cosmological solutions in f(R)-gravity is discussed. Instead of taking into account phenomenological models, we assume, as a physical criterium, the existence of Noether symmetries in the cosmological…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this…
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…
We study in which conditions the Hyperextended Scalar Tensor theory in an FLRW background admits a Noether symmetry and derive the vectors field generating it.
In this paper, we develop basic results of algebraic geometry over abelian symmetric monoidal categories. Let $A$ be a commutative monoid object in an abelian symmetric monoidal category $(\mathbf C,\otimes,1)$ satisfying certain conditions…
We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent variables are in one-to-one correspondence with the…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the classification of those two-field cosmological models which admit such symmetries.
A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries,…
We construct the deformed generators of Schroedinger symmetry consistent with noncommutative space. The examples of the free particle and the harmonic oscillator, both of which admit Schroedinger symmetry, are discussed in detail. We…
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…
Symmetry plays a crucial role in theoretical physics, especially Noether symmetry, which is a powerful approach for identifying the models at the fundamental level. The exact solution is provided within the point-like Lagrangian framework.…
We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by…
Extended $f(R)$ theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended $f(R)$ theories: $f(R,T)$ theory, in which curvature is coupled non…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…