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Classical W-gravities and the corresponding quantum theories are reviewed. W-gravities are higher-spin gauge theories in two dimensions whose gauge algebras are W-algebras. The geometrical structure of classical W-gravity is investigated,…
Soft theorems in gauge theory and gravity encode the universal properties of scattering amplitudes as the zero frequency limit of one or more external states is approached. When the participating particles are treated in the massless limit,…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
We discuss how the symmetries of $\kappa$-Minkowski non-commutative spacetime can be described by the $\kappa$-Poincar\'e Hopf algebra. In particular, we focus on a generalization of the Noether analysis in the $\kappa$-deformed framework…
We consider self-interacting, perturbative quantum field theory in a curved spacetime background with a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether…
This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as…
We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables correspond to the equations governing the activation dynamics…
We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are…
Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent $z=1$, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be directly read off from the Lie algebra…
Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
We consider a broad class of systems of nonlinear integro-differential equations posed on the real line that arise as Euler-Lagrange equations to energies involving nonlinear nonlocal interactions. Although these equations are not readily…
By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given…
We discuss Ward identities for strongly interacting fermion systems described by Eliashberg-type theories. We show that Ward identities are not in conflict with Migdal theorem. We derive diagrammatically Ward identity for a charge vertex in…
We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that…
This paper investigates the geometry of compact stellar objects via Noether symmetry strategy in the framework of curvature-matter coupled gravity. For this purpose, we assume the specific model of this theory to evaluate Noether equations,…
In any diffeomorphism invariant theory of gravity, one can define a Noether charge arising from the invariance of the Lagrangian under diffeomorphisms. We have determined the Noether charge for scalar-tensor theories of gravity, in which…
This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian,…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the…