Related papers: A General Criterion of Quantum Integrability Accom…
Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of nonintegrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric…
We discuss the generalization of the local renormalization group approach to theories in which Weyl symmetry is gauged. These theories naturally correspond to scale invariant - rather than conformal invariant - models in the flat space…
We study quantum gravity in $2+\epsilon$ dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the…
The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this…
One of the common features in all promising candidates of quantum gravity is the existence of a minimal length scale, which naturally emerges with a generalized uncertainty principle, or equivalently a modified commutation relation.…
We introduce the definition of the typical irreducible modules of the generalized quantum groups, and prove the Weyl-Kac-type formulas of their characters. As a by-product, we obtain the Weyl-Kac-type character formulas of the typical…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and Box R, with coefficients, properly normalized, called c, a and a', the latter being ambiguously defined by…
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
We study the consistency of orbifold field theories and clarify to what extent the condition of having an anomaly-free spectrum of zero-modes is sufficient to guarantee it. Preservation of gauge invariance at the quantum level is possible,…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
In the asymptotic safety paradigm, a quantum field theory reaches a regime with quantum scale invariance in the ultraviolet, which is described by an interacting fixed point of the Renormalization Group. Compelling hints for the viability…
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals.…