Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Kinematics and Energetics of Nut-Cracking in Wild Capuchin Monkeys (Cebus libidinosus) in Piaui, Brazil

Wild bearded capuchins (Cebus libidinosus, quadrupedal, medium-sized monkeys) crack nuts using large stones. We examined the kinematics and energetics of the nut-cracking action of two adult males and two adult females. From a bipedal stance, the monkeys raised a heavy hammer stone (1.46 and 1.32 kg, from 33 to 77% of their body weight) to an average height of 0.33 m, 60% of body length. Then, they rapidly lowered the stone by flexing the lower extremities and the trunk until the stone contacted the nut. A hit consisting of an upward phase and a downward phase averaged 0.74 s in duration. The upward phase lasted 69% of hit duration. All subjects added discernable energy to the stone in the downward phase. The monkeys exhibited individualized kinematic strategies, similar to those of human weight lifters. Capuchins illustrate that human-like bipedal stance and large body size are unnecessary to break tough objects from a bipedal position. The phenomenon of bipedal nut-cracking by capuchins provides a new comparative reference point for discussions of percussive tool use and bipedality in primates. Am J Phys Anthropol 138:210-220, 2009. (C) 2008 Wiley-Liss, Inc.

Inhomogeneous Fermi and quantum spin systems on lattices

We study the thermodynamic properties of a certain type of space-inhomogeneous Fermi and quantum spin systems on lattices. We are particularly interested in the case where the space scale of the inhomogeneities stays macroscopic, but very small as compared to the side-length of the box containing fermions or spins. The present study is however not restricted to "macroscopic inhomogeneities" and also includes the (periodic) microscopic and mesoscopic cases. We prove that - as in the homogeneous case - the pressure is, up to a minus sign, the conservative value of a two-person zero-sum game, named here thermodynamic game. Because of the absence of space symmetries in such inhomogeneous systems, it is not clear from the beginning what kind of object equilibrium states should be in the thermodynamic limit. However, we give rigorous statements on correlations functions for large boxes. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4763465]

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

The legs: a key to bird evolutionary success

Birds are the most diverse and largest group of extant tetrapods. They show marked variability, yet much of this variation is superficial and due to feather and bill color and shape. Under the feathers, the skeleto-muscular system is rather constant throughout the bird group. The adaptation to flight is the explanation for this uniformity. The more obvious morphological adaptations for flight are the wings, but the trunk is always rigid, the tail is short and the neck is flexible, since all these features are correlated with flying behaviour. Unrelated to the exigencies of flight, the legs always have three long bones, and all the birds walk on their toes. This leg structure is a striking plesiomorphic feature that was already present in related dinosaurs. The multi-purpose potential of the legs is the result of the skeletal architecture of a body with three segmented flexed legs. This configuration provides mechanical properties that allow the use of the legs as propulsive, paddling, foraging or grooming tools. It is the association of diverse modes of locomotion-walking, running, hopping, flying and swimming-that have enabled the birds to colonize almost all the environments on Earth.

Dynamical (super)symmetry vacuum properties of the supersymmetric Chern-Simons-matter model

By computing the two-loop effective potential of the D=3 N=1 supersymmetric Chern-Simons model minimally coupled to a massless self-interacting matter superfield, it is shown that supersymmetry is preserved, while the internal U(1) and the scale symmetries are broken at two-loop order, dynamically generating masses both for the gauge superfield and for the real component of the matter superfield.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Detection of gait perturbations based on proprioceptive information. Application to Limit Cycle Walkers

Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans': Neither trajectory controlled robots, nor dynamic walking machines (Limit CycleWalkers) are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.

Theoretical study of the XP3 (X = Al, B, Ga) clusters

The lowest singlet and triplet states of AlP3, GaP3 and BP3 molecules with C-s, C-2v and C-3v symmetries were characterized using the B3LYP functional and the aug-cc-pVTZ and aug-cc-pVQZ correlated consistent basis sets. Geometrical parameters and vibrational frequencies were calculated and compared to existent experimental and theoretical data. Relative energies were obtained with single point CCSD(T) calculations using the aug-cc-pVTZ, aug-cc-pVQZ and aug-cc-pV5Z basis sets, and then extrapolating to the complete basis set (CBS) limit. (C) 2011 Elsevier B.V. All rights reserved.

A rationale for long-lived quarks and leptons at the LHC: low energy flavour theory

In the framework of gauged flavour symmetries, new fermions in parity symmetric representations of the standard model are generically needed for the compensation of mixed anomalies. The key point is that their masses are also protected by flavour symmetries and some of them are expected to lie way below the flavour symmetry breaking scale(s), which has to occur many orders of magnitude above the electroweak scale to be compatible with the available data from flavour changing neutral currents and CP violation experiments. We argue that, actually, some of these fermions would plausibly get masses within the LHC range. If they are taken to be heavy quarks and leptons, in (bi)-fundamental representations of the standard model symmetries, their mixings with the light ones are strongly constrained to be very small by electroweak precision data. The alternative chosen here is to exactly forbid such mixings by breaking of flavour symmetries into an exact discrete symmetry, the so-called proton-hexality, primarily suggested to avoid proton decay. As a consequence of the large value needed for the flavour breaking scale, those heavy particles are long-lived and rather appropriate for the current and future searches at the LHC for quasi-stable hadrons and leptons. In fact, the LHC experiments have already started to look for them.

Constraining anomalous Higgs boson interactions

The recently announced Higgs boson discovery marks the dawn of the direct probing of the electroweak symmetry breaking sector. Sorting out the dynamics responsible for electroweak symmetry breaking now requires probing the Higgs boson interactions and searching for additional states connected to this sector. In this work, we analyze the constraints on Higgs boson couplings to the standard model gauge bosons using the available data from Tevatron and LHC. We work in a model-independent framework expressing the departure of the Higgs boson couplings to gauge bosons by dimension-six operators. This allows for independent modifications of its couplings to gluons, photons, and weak gauge bosons while still preserving the Standard Model (SM) gauge invariance. Our results indicate that best overall agreement with data is obtained if the cross section of Higgs boson production via gluon fusion is suppressed with respect to its SM value and the Higgs boson branching ratio into two photons is enhanced, while keeping the production and decays associated to couplings to weak gauge bosons close to their SM prediction.

Ward identities in Lifshitz-like field theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z = 2 in six spatial dimensions.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.