Who`s My Neighbour?

The EU is approaching bordering countries offering them Òneighbourhood relationsÓ, but it fails short of taking into consideration how this concept may be perceived by its partners. This paper will propose a reconsideration of the term ÒneighbourÓ in the conviction that this operation is of fundamental importance in order to solve any eventual misunderstanding on its meaning and to define, in the context of the ENP, what the nature of a relationship of neighbourhood may imply. In particular, it will look at the literature to show that this term, far from being uncontested, fundamentally implies an ÒotheringÓ practice which transcends the Christian teaching to Òlove oneÕs neighbour as oneselfÓ. Then, it will underline that this word may have different connotations in partner countries which may go beyond a neutral indication of geographical proximity and which may not correspond to the meaning consolidated in the Anglo Saxon tradition which basically refers to a neighbour as to a ÒfellowÓ. Finally, the paper will underline that the same fundamental ambiguity which marks the term here considered lies at the very core of the ENP. As a matter of fact, this policy shows persisting uncertainties on how to substantiate the relationship with neighbouring countries, whether in terms of fellowship and integration or in terms of an Òother than meÓ who still represents a security threat.Neighbourhood, ENP, integration-security dilemma

The Yangian Symmetry of the Hubbard Models with Variable Range Hopping

We present two pairs of Y($sl_2$) Yangian symmetries for the trigonometric and hyperbolic versions of the Hubbard model with non-nearest-neighbour hopping. In both cases the Yangians are mutually commuting, hence can be combined into a Y($sl_2$)$\oplus$Y($sl_2$) Yangian. Their mutual commutativity is of dynamical origin. The known Yangians of the Haldane-Shastry spin chain and the nearest neighbour Hubbard model are contained as limiting cases of our new representations.Comment: 10 pages, Late

Causal Fermions in Discrete Spacetime

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.Comment: 16 pages, 1 figur