Baby universes and worldline field theories

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.

p-form surface charges on AdS: renormalization and conservation

Surface charges of a p-form theory on the boundary of an AdSd+1 spacetime are computed. Counter-terms on the boundary produce divergent corner-terms which holographically renormalize the symplectic form. Different choices of boundary conditions lead to various expressions for the charges and the associated fluxes. With the usual standard AdS boundary conditions, there are conserved zero-mode charges. Moreover, we explore two leaky boundary conditions which admit an infinite number of charges forming an Abelian algebra and non-vanishing flux. Finally, we discuss magnetic p-form charges and electric/magnetic duality.

Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity

We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the symplectic structure by a surface contribution appearing in addition to the standard bulk piece. The Poincaré transformations have then well-defined (integrable, finite) canonical generators. Moreover, improper fermionic gauge symmetries, which are also well-defined canonical transformations, are further enlarged and turn out to be parametrized by two independent angle-dependent spinor functions at infinity, which lead to an infinite-dimensional fermionic algebra endowed with a central charge. We extend next the analysis to the supersymmetric spin-(1, 3/2) and spin-(2, 3/2) multiplets. First, we present the canonical realization of the super-Poincaré algebra on the spin-(1, 3/2) multiplet, which is shown to be consistently enhanced by the infinite-dimensional abelian algebra of angle-dependent bosonic and fermionic improper gauge symmetries associated with the electromagnetic and the Rarita-Schwinger fields, respectively. A similar analysis of the spin-(2, 3/2) multiplet is then carried out to obtain the canonical realization of the super-Poincaré algebra, consistently enhanced by the abelian improper bosonic gauge transformations of the spin-2 field (BMS supertranslations) and the abelian improper fermionic gauge transformations of the spin-3/2 field.

On extension of classical Baer results to Poisson algebras

In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the nth hypercenter of a Poisson algebra P (over some specific field) has a finite codimension and P does not contain zero divisors, then P is an abelian algebra.

Some Structural Properties of Semidirect Sums of \(\mathfrak{so}(3)\) and Abelian Lie Algebras

Various structural properties of semidirect sums of the rotation Lie algebra of rank one and an Abelian algebra described in terms of real representations with at most two irreducible constituents are obtained. The stability properties of these semidirect sums are studied by means of the cohomological and the Jacobi scheme methods.

Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations

Coupled systems of Lane–Emden equations are of considerable interest as they model several physical phenomena, for instance population evolution, pattern formation, and chemical reactions. Assuming a complex variational structure, we classify the generalized system of Lane–Emden type equations in relation to Noether-like operators and associated first integrals. Various forms of functions appearing in the considered system are taken, and it is observed that the Noether-like operators form an Abelian algebra for the corresponding Euler–Lagrange-type systems. Interestingly, we find that in many cases, the Noether-like operators satisfy the classical Noether symmetry condition and become the Noether symmetries. Moreover, we observe that the classical Noetherian integrals and the first integrals we determine using the complex Lagrangian approach turn out to be the same for the underlying system of Lane–Emden equations.

Dynamics of algebras in quantum unstable systems

We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and represent the time evolution of quantum observables in the Heisenberg picture, in such a way that time evolution is nonunitary. This allows to describe observables that are initially noncommutative, but become commutative after time evolution. In other words, a non-abelian algebra of relevant observables becomes abelian when times goes to infinity. We finally present some relevant examples.

Breaking Symmetry Effects on Heavy Tetraquarks

In this contribution we present symmetry arguments that can be applied to study the stability of four-quark systems with two different masses. The role played by different symmetry breaking effects and the non-Abelian algebra of color forces is discussed in detail. In the particular case of hidden-flavor all-heavy four-quark states, [Formula: see text], the system becomes unstable for standard color-additive models. Differences and similarities between [Formula: see text] and [Formula: see text] configurations are presented. In the latter case, its stability when the mass ratio [Formula: see text] increases was established almost forty years ago. In the former case, we find a kind of metastability between the lowest threshold, [Formula: see text] and the highest one, [Formula: see text].