The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.

Aim The relative contribution of community functional diversity and composition to ecosystem functioning is a critical question in ecology in order to enable better predictions of how ecosystems may respond to a changing climate.However, there is little consensus about which modes of functional biodiversity are most important for tree growth at large spatial scales. Here we assessed the relative importance of climate, functional diversity and functional identity (i.e. the communitymeanvalues of four key functional traits) for tree growth across the European continent, spanning the northern boreal to the southern Mediterranean forests. Location Finland, Germany, Sweden, Spain and Wallonia (Belgium). Methods Using data from five European national forest inventories we applied a hierarchical linear model to estimate the sensitivity of tree growth to changes in climate, functional diversity and functional identity along a latitudinal gradient. Results Functional diversity was weakly related to tree growth in the temperate and boreal regions and more strongly in the Mediterranean region. In the temperate region, where climate was the most important predictor, functional diversity and identity had a similar importance for tree growth. Functional identity was strongest at the latitudinal extremes of the continent, largely driven by strong changes in the importance of maximum height along the latitudinal gradient. Main conclusions Functional diversity is an important driver of tree growth in the Mediterranean region, providing evidence that niche complementarity may be more important for tree growth in water-limited forests. The strong influence of functional identity at the latitudinal extremes indicates the importance of a particular trait composition for tree growth in harsh climates. Furthermore, we speculate that this functional identity signal may reflect a trait-based differentiation of successional stages rather than abiotic filtering due to water or energy limitation

Abstract.The consistency of quantum field theories defined on domains with external borders imposes very restrictive constraints on the type of boundary conditions that the fields can satisfy. We analyse the global geometrical and topological properties of the space of all possible boundary conditions for scalar quantum field theories. The variation of the Casimir energy under the change of boundary conditions reveals the existence of singularities generically associated to boundary conditions which either involve topology changes of the underlying physical space or edge states with unbounded below classical energy. The effect can be understood in terms of a new type of Maslov index associated to the non-trivial topology of the space of boundary conditions. We also analyze the global aspects of the renormalization group flow, T-duality and the conformal invariance of the corresponding fixed points.

The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories pseudoperiodic and quasiperiodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. On the contrary, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.

In this paper the quantum vacuum energies induced by massive fluctuations of one real scalar field on a configuration of two partially transparent plates are analysed. The physical properties of the infinitely thin plates are characterized by two Dirac-δ potentials. We find that an attractive/repulsive Casimir force arises between the plates when the weights of the δ's have equal/different sign. If some of the plates absorbs fluctuations below some threshold of energy (the corresponding weight is negative) there is the need to set a minimum mass to the scalar field fluctuations to preserve unitarity in the corresponding quantum field theory. Two repulsive δ-interactions are compatible with massless fluctuations. The effect of Dirichlet boundary conditions at the endpoints of the interval (−a, a) on a massless scalar quantum field theory defined on this interval is tantamount letting the weights of the repulsive δ-interactions to +∞.