Gauge Model Research Articles

Polymer optical fiber strain gauge for human-robot interaction forces assessment on an active knee orthosis

Abstract This paper presents the development of a polymer optical fiber (POF) strain gauge based on the light coupling principle, which the power attenuation is created by the misalignment between two POFs. The misalignment, in this case, is proportional to the strain on the structure that the fibers are attached. This principle has the advantages of low cost, ease of implementation, temperature insensitiveness, electromagnetic fields immunity and simplicity on the sensor interrogation and signal processing. Such advantages make the proposed solution an interesting alternative to the electronic strain gauges. For this reason, an analytical model for the POF strain gauge is proposed and validated. Furthermore, the proposed POF sensor is applied on an active orthosis for knee rehabilitation exercises through flexion/extension cycles. The controller of the orthosis provides 10 different levels of robotic assistance on the flexion/extension movement. The POF strain gauge is tested at each one of these levels. Results show good correlation between the optical and electronic strain gauges with root mean squared deviation (RMSD) of 1.87 Nm when all cycles are analyzed, which represents a deviation of less than 8%. For the application, the proposed sensor presented higher stability than the electronic one, which can provide advantages on the rehabilitation exercises and on the inner controller of the device.

Orthogonal bases of invariants in tensor models

Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd = U(N1) ⊗ · · · ⊗ U(Nd) . We show that there are two natural ways of counting invariants, one for arbitrary Gd and another valid for large rank of Gd. We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of Gd diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.

Scaled lattice fermion fields, stability bounds, and regularity

We consider locally gauge-invariant lattice quantum field theory models with locally scaled Wilson-Fermi fields in d = 1, 2, 3, 4 spacetime dimensions. The use of scaled fermions preserves Osterwalder-Seiler positivity and the spectral content of the models (the decay rates of correlations are unchanged in the infinite lattice). In addition, it also results in less singular, more regular behavior in the continuum limit. Precisely, we treat general fermionic gauge and purely fermionic lattice models in an imaginary-time functional integral formulation. Starting with a hypercubic finite lattice Λ⊂(aZ)d, a ∈ (0, 1], and considering the partition function of non-Abelian and Abelian gauge models (the free fermion case is included) neglecting the pure gauge interactions, we obtain stability bounds uniformly in the lattice spacing a ∈ (0, 1]. These bounds imply, at least in the subsequential sense, the existence of the thermodynamic (Λ ↗ (aZ)d) and the continuum (a ↘ 0) limits. Specializing to the U(1) gauge group, the known non-intersecting loop expansion for the d = 2 partition function is extended to d = 3 and the thermodynamic limit of the free energy is shown to exist with a bound independent of a ∈ (0, 1]. In the case of scaled free Fermi fields (corresponding to a trivial gauge group with only the identity element), spectral representations are obtained for the partition function, free energy, and correlations. The thermodynamic and continuum limits of the free fermion free energy are shown to exist. The thermodynamic limit of n-point correlations also exist with bounds independent of the point locations and a ∈ (0, 1], and with no n! dependence. Also, a time-zero Hilbert-Fock space is constructed, as well as time-zero, spatially pointwise scaled fermion creation operators which are shown to be norm bounded uniformly in a ∈ (0, 1]. The use of our scaled fields since the beginning allows us to extract and isolate the singularities of the free energy when a ↘ 0.

Dynamic scaling of topological ordering in classical systems

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional $\mathbb{Z}_2$ (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a non-local order parameter (defined using Wilson loops) and a dynamic exponent $z=2.70 \pm 0.03$, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature---the Ising chain, the two-dimensional $\mathbb{Z}_2$ gauge model, and a three-dimensional star model (another variant of the $\mathbb{Z}_2$ gauge model). In these systems the correlation length diverges exponentially, in a way that is non-smooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.

Mass problem in the Standard Model

We propose a new SU(3)C ⊗ SU(2)L ⊗ U(1)Y ⊗ U(1)X gauge model which is non universal respect to the three fermion families of the Standard Model. We introduce additional one top-like quark, two bottom-like quarks and three right handed neutrinos in order to have an anomaly free theory. We also consider additional three right handed neutrinos which are singlets respect to the gauge symmetry of the model to implement see saw mechanism and give masses to the light neutrinos according to the neutrino oscillation phenomenology. In the context of this horizontal gauge symmetry we find mass ansatz for leptons and quarks. In particular, from the analysis of solar, atmospheric, reactor and accelerator neutrino oscillation experiments, we get the allow region for the Yukawa couplings for the charge and neutral lepton sectors according with the mass squared differences and mixing angles for the two neutrino hierarchy schemes, normal and inverted.

Duals of U(N) LGT with staggered fermions

Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions. Applications related to the finite temperature/density QCD are discussed.

The Unified Gauge Model of Four Interactions

We have reestablished the SU (5) grand unified model according to new research results in order to clarify some misunderstandings to the model. On this basis the unified gauge model describing four interactions containing gravity has been established, and its results are consistent with experiments.

A two-dimensional soliton system of vortex and Q-ball

The (2+1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and a Q-ball. This two-dimensional system is electrically neutral, nevertheless it possesses a nonzero electric field. Moreover, the soliton system has a quantized magnetic flux and a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of topological and nontopological solitons.

Gauge leptoquark as the origin of B -physics anomalies

The vector leptoquark representation, $U_\mu = (3,1,2/3)$, was recently identified as an exceptional single mediator model to address experimental hints on lepton flavour universality violation in semileptonic $B$-meson decays, both in neutral ($b \to s \mu \mu$) and charged ($b \to c \tau \nu$) current processes. Nonetheless, it is well-known that massive vectors crave an ultraviolet (UV) completion. We present the first full-fledged UV complete and calculable gauge model which incorporates this scenario while remaining in agreement with all other indirect flavour and electroweak precision measurements, as well as, direct searches at high-$p_T$. The model is based on a new non-abelian gauge group spontaneously broken at the TeV scale, and a specific flavour structure suppressing flavour violation in $\Delta F = 2$ processes while inducing sizeable semileptonic transitions.

Excitation basis for (3+1)d topological phases

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev’s quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu’s tube algebra. This defines an algebraic structure extending the Drinfel’d double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form varSigma times {mathbb{S}}_1 , with Σ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass and a Gaussian phase glass. The first two models, describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field while the last two describe the effects of random negative Josephson-junction couplings or $\pi$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge and flux glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin film superconductors in a magnetic field, in the large disorder limit.

Holomorphic scalar portals and the OPE

Visible-sector SUSY-breaking effects are computed in terms of hidden-sector correlation functions for generic holomorphic scalar portals. The solutions, which are valid irrespective of the hidden-sector dynamics, are approximated with the help of the operator product expansion (OPE). Indeed, for theories with superconformal symmetry at high energy, the superconformal OPE formalism can be used to disentangle the high-energy dynamics, encoded in the OPE coefficients, from the low-energy dynamics of the SUSY-breaking vacuum expectation values. A systematic method is proposed to compute the OPE coefficients, using relations between correlation functions of superfields and correlation functions of their quasi-primary component fields. The method, which is quite general, could be useful in building models of gauge- or gravity-mediated SUSY breaking and in analysing the viability of such models in a systematic way.

Towards a phase diagram for spin foams

One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin foams. This scheme is based on the concept of decorated tensor networks, which have been introduced recently. Here we develop an algorithm applicable to gauge theories with non-Abelian groups, which for the first time allows for the application of tensor network coarse-graining techniques to proper spin foams. The procedure deals efficiently with the large redundancy of degrees of freedom resulting from gauge invariance. The algorithm is applied to 3D spin foams defined on a cubical lattice which, in contrast to a proper triangulation, allows for non-trivial simplicity constraints. This mimics the construction of spin foams for 4D gravity. For lattice gauge models based on a finite group we use the algorithm to obtain phase diagrams, encoding the continuum limit of a wide range of these models. We find phase transitions for various families of models carrying non-trivial simplicity constraints.

Inception of self-interacting dark matter with dark charge conjugation symmetry

A new understanding of the stability of self-interacting dark matter is pointed out, based on the simplest spontaneously broken Abelian U(1) gauge model with one complex scalar and one Dirac fermion. The key is the imposition of dark charge conjugation symmetry. It allows the possible existence of two stable particles: the Dirac fermion and the vector gauge boson which acts as a light mediator for the former's self-interaction. Since this light mediator does not decay, it avoids the strong cosmological constraints recently obtained for all such models where the light mediator decays into standard-model particles.

A coherent quantum annealer with Rydberg atoms

There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner–Hauke–Zoller (LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a platform for quantum annealing. In LHZ an infinite-range spin-glass is mapped onto the low energy subspace of a spin-1/2 lattice gauge model with quasi-local four-body parity constraints. This spin model can be emulated in a natural way with Rubidium and Caesium atoms in a bipartite optical lattice involving laser-dressed Rydberg–Rydberg interactions, which are several orders of magnitude larger than the relevant decoherence rates. This makes the exploration of coherent quantum enhanced optimization protocols accessible with state-of-the-art atomic physics experiments.

Embedding cosmological inflation, axion dark matter and seesaw mechanism in a 3-3-1 gauge model

The Peccei–Quinn symmetry is an intrinsic global symmetry of the 3-3-1 gauge models. Its spontaneous breaking mechanism engendering an invisible KSVZ-like axion links the 3-3-1 models with new physics at ∼1010 GeV scale. The axion that results from this mechanism is an interesting candidate for the dark matter of the universe, while its real partner may drive inflation if radiative corrections are taken into account. This is obtained by connecting the type I seesaw mechanism with the spontaneous breaking of the Peccei–Quinn symmetry. In the end of the day we have a scenario providing a common answer to the strong-CP problem, inflation, dark matter and neutrino mass.

Defining relations for the orbit type strata of SU(2)-lattice gauge models

We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining relations for the orbit type strata in the reduced classical phase space. The latter is realized as a certain quotient of a direct product of copies of the complexified group SL(2,\CC) (sometimes named the GIT-quotient because it provides a categorical quotient in the sense of geometric invariant theory). The relations derived can be used for the construction of the orbit type costratification of the Hilbert space of the quantum system in the sense of Huebschmann.

Normal wave diffraction on a plate submerged in a liquid: Level gauge model, factorization method modification, and waveguide quasiresonances

An exact solution is obtained for onemore new diffraction problem whose transcendental difficulty has been known since Sommerfeld and Kirchhoff. The model of waveguide level gauge, where the main problem is the bulk diffraction of normal waves in a layered structure consisting of an elastic plate between two semi-infinite liquid layers, is investigated. The boundary value problem is solved by using a modification of the Wiener–Hopf factorization method; the factorization is used twice to solve two systems of underdetermined functional equations, and this is a specific characteristics of the problem and amethodological novelty. The proposed modification is acceptable for the class of such problems. The diffracted spectra are analyzed; the waveguide quasiresonances are physically treated; the effect of pure Lamb wave propagation under the liquid is established; the narrow-band backward-wave modes are determined.

BPS states in [formula omitted] supersymmetric G2 and F4 models

In BPS quiver theory of N=2 supersymmetric pure gauge models with gauge invariance G, primitive BPS quivers Q0G are of two types: Q0ADE and Q0BCFG. In this study, we first show that Q0ADE have outer-automorphism symmetries inherited from the outer-automorphisms of the Dynkin diagrams of ADE Lie algebras. Then, we extend the usual folding operation of Dynkin diagrams ADE→BCFG to obtain the two following things: (i) relate Q0BCFG quivers and their mutations to the Q0ADE ones and their mutations; and (ii) link the BPS chambers of the N=2ADE theories with the corresponding BCFG ones. As an illustration of this construction, we derive the BPS and anti-BPS states of the strong chambers QstgG2 and QstgF4 of the 4d N=2 pure G2 and F4 gauge models.

Gauge model of a crack

The paper proposes a model of a crack system as local symmetry breaking for a group of 3D rotations compensated by fictitious fields that make Lagrangian equations of elastic energy density covariant in the effective Riemannian space. Equilibrium equations are solved using the perturbation theory with the number of notches being a small parameter, and exact expressions are derived for stress and gauge fields in a 2D problem by applying Hilbert transform to orthogonal Chebyshev polynomials. The model is generalized to nonlinear elasticity (deformation theory of plasticity) and statistical mesomechanics models. Also presented is a solution for stress concentration in a system of arbitrarily oriented cracks which takes into account their mutual influence at any order of the perturbation theory and reduces to a system of linear equations with explicit exact solutions.