Nonlinear Realization Research Articles

Impossible symmetries and conformal gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity. Published by the American Physical Society 2024

Electric dipole moments in 5+3 flavor weak effective theory

A fully generic treatment of electric dipole moments (EDMs) is presented in the CP-violating and flavor-conserving weak effective field theory (WET) with five flavors of quarks and three flavors of leptons. We systematically analyze leading contributions to EDMs originating from QCD and QED renormalization group running between the electroweak scale and low energy scales of about 2 GeV. We include the full one-loop anomalous dimension and a subset of two-loop corrections, as well as threshold corrections at the bottom, charm and τ masses. This allows us to derive master formulae in the space of generic WET for the neutron and proton EDMs, for EDMs of diamagnetic atoms, and for the precession frequencies constrained in molecular EDM experiments, from which bounds on the electron EDM are extracted. In particular, our master formulae capture the contributions of WET CP-violating operators with heavy quark and lepton flavors. As an application, we study EDM constraints on the Yukawa couplings of the Higgs boson, in both the linear and non-linear realizations of electroweak symmetry breaking.

Vibration suppression of a platform by a fractional type electromagnetic damper and inerter-based nonlinear energy sink

The theory of linear and nonlinear dynamic vibration absorbers is a well-established topic for many years. However, many recent contributions paid attention to the nonlinear vibration absorbers and different practical realizations of corresponding devices. Here, we propose a mechanical system constituted of the inerter-based nonlinear energy sink attached to the main body that is resting on an elastic foundation and is grounded through the fractional type electromagnetic damper. The two-degree-of-freedom system is described via two coupled differential equations with one of them having a fractional-order derivative term and the other one containing cubic stiffness nonlinearity. The incremental harmonic balance (IHB) method is employed to solve the equations and studies the strongly nonlinear periodic responses of the system. Applied approximated solution methodology is validated by the numerical Newmark method adapted to deal with the system of nonlinear fractional-order differential equations. The appropriate and necessary number of harmonics used in the IHB solution is commented and validated. This study can be a first step in understanding the dynamics and giving directions for the future design of vibration-isolating platforms based on inerter-based nonlinear vibration absorbers and electromagnetic dampers.

TT¯ deformation of N=(1,1) off-shell supersymmetry and partially broken supersymmetry

We construct the superaction for the TT¯ deformation of 2D free N=(1,1) supersymmetric model with a deformed superfield. We show that the N=(1,1) off-shell supersymmetry in the free theory is deformed under the TT¯ deformation, which is incorporated in the deformed superfield. We interpret this superaction as an effective action of the Goldstone superfield for the partial spontaneous breaking of N=(2,2) supersymmetry to N=(1,1). We show that the unbroken and broken supersymmetry of the effective superaction corresponds to the off-shell N=(1,1) supersymmetry and the off-shell Fermi global nonlinear symmetry in the TT¯-deformed theory, respectively. We demonstrate that this effective superaction can be obtained by the nonlinear realization of the partially broken global supersymmetry (PBGS) from the coset superspace. Furthermore, we reproduce the superaction by the constrained superfield method accompanied by a field redefinition. Published by the American Physical Society 2024

Diffeomorphic structure of evolution equations

In this work the problem of the consistent treatment of multidimensional quadratic Hamiltonians is analyzed and developed from the geometric point of view. To this end, two approaches to the treatment for the problem are studied and developed: the pure matrix representation that involves Madelung type transforms (maps), and the evolution type based in a group manifold endowed with the symplectic groups and their coverings. Some of our goals is to introduce important geometric and group theoretical tools in the proposed approaches, such as Fermi normal coordinates in the first and a generalization of the method of nonlinear realizations in the second one. Several interesting results appear and some examples of application of these concepts in different physical scenarios are developed and presented such as the relationship with the Zeldovich approximation for the dynamic of large-scale cosmological structure, the classic case of Gertsner waves or the evolution problem with an inverted Hamiltonian of Caldirola-Kanai type.

Multiplexable all-optical nonlinear activator for optical computing

As an alternative solution to surpass electronic neural networks, optical neural networks (ONNs) offer significant advantages in terms of energy consumption and computing speed. Despite the optical hardware platform could provide an efficient approach to realizing neural network algorithms than traditional hardware, the lack of optical nonlinearity limits the development of ONNs. Here, we proposed and experimentally demonstrated an all-optical nonlinear activator based on the stimulated Brillouin scattering (SBS). Utilizing the exceptional carrier dynamics of SBS, our activator supports two types of nonlinear functions, saturable absorption and rectified linear unit (Relu) models. Moreover, the proposed activator exhibits large dynamic response bandwidth (∼11.24 GHz), low nonlinear threshold (∼2.29 mW), high stability, and wavelength division multiplexing identities. These features have potential advantages for the physical realization of optical nonlinearities. As a proof of concept, we verify the performance of the proposed activator as an ONN nonlinear mapping unit via numerical simulations. Simulation shows that our approach achieves comparable performance to the activation functions commonly used in computers. The proposed approach provides support for the realization of all-optical neural networks.

Origin of higher Schwarzians

In this paper we analyze higher Schwarzians and show that they are closely related to the nonlinear realization of the Virasoro algebra. The Goldstone fields of such a realization provide a new set of SL(2,R) invariant higher Schwarzians that are deeply related to those of Aharonov [], Tamanoi [], and Bonora-Matone [; ; ]. A minor change of the coset space parametrization leads to a new set of SL(2,R) noninvariant higher Schwarzians now related to the Schippers [] and Bertilsson [] Schwarzians. Published by the American Physical Society 2024

Evolution of physical systems and nonlinear realized symmetries

In this work, a new method to determine and to describe the evolution of physical systems (in classical or quantum regimes) is proposed. The main idea is based in the observation that the complete determination of dynamics of the system is connected to the nonlinear realization (NLR) of the symmetry group associated with the symmetry of the Hamiltonian [Formula: see text] of the system. The Maurer–Cartan forms, when they are parametrically associated to the projection on the hypersurface induced by the group in question via pullback, of the Hamiltonian components (based on the generators of the symmetry group by which it is defined) give rise to a fundamental system of equations by which the precise evolution can be determined. Such a system of equations under certain conditions that we will specify in this paper coincides with the system obtained through the Wei–Norman method, thus showing explicitly that our proposal is more general due the universal character of equations from the NLRs approach. As example, the important problem of the Caldirola–Kanai inverted Hamiltonian is completely solved, showing at the same time a new interpretation of what NLRs refer to.

Non-Lorentzian expansions of the Lorentz force and kinematical algebras

We consider non-Lorentzian expansions, Galilean and Carrollian, of the Lorentz force equation in which both the particle position and the electro-magnetic field are expanded. There are two well-known limits in the case of a constant field, called electric and magnetic, that are studied separately. We show that the resulting equations of motion follow equivalently from considering a non-linear realisation of a certain infinite-dimensional algebras.

Non-Lorentzian IIB supergravity from a polynomial realization of SL(2, ℝ)

We derive the action and symmetries of the bosonic sector of non-Lorentzian IIB supergravity by taking the non-relativistic string limit. We find that the bosonic field content is extended by a Lagrange multiplier that implements a restriction on the Ramond-Ramond fluxes. We show that the SL(2, ℝ) transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear polynomial realization. Using classical invariant theory of polynomial equations and binary forms, we will develop a general formalism describing the polynomial realization of SL(2, ℝ) and apply it to the special case of non-Lorentzian IIB supergravity. Using the same formalism, we classify all the relevant SL(2, ℝ) invariants. Invoking other bosonic symmetries, such as the local boost and dilatation symmetry, we show how the bosonic part of the non-Lorentzian IIB supergravity action is formed uniquely from these SL(2, ℝ) invariants. This work also points towards the concept of a non-Lorentzian bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to bootstrap the bosonic dynamics in Lorentzian supergravity, without considering the fermions.

Heavy resonances and the oblique parameters S and T

It has been confirmed experimentally the existence of a mass gap between Standard Model (SM) and eventual Beyond Standard Model (BSM) fields. Therefore, the use of effective approaches to search for fingerprints of New Physics is very appealing. A non-linear realizations of the Electroweak Symmetry Breaking is considered here, where the Higgs is a singlet with free couplings and the SM fields are also coupled to bosonic heavy resonances. A one-loop-level calculation of the oblique S and T parameters is presented here. This analysis allows us to constrain resonance masses to be above the TeV scale, ▪TeV, in good agreement with our previous determinations, where these observables were computed with a more simplified Lagrangian.

Particle realization of Bondi-Metzner-Sachs symmetry in 2 + 1 space-time

We construct a Lorentz invariant massive particle model in (2+1) space-time with an enlarged set of symmetries which includes Bondi-Metzner-Sachs (BMS) translations (supertranslations), using the non-linear realization framework. The Hamiltonian formalism for the resulting Lagrangian is constructed, and the infinite phase-space constraints and the set of gauge transformations are analysed. We also compute the massless limit of the theory in phase-space. After eliminating the gauge degrees of freedom, the physical reduced space is left only with the degrees of freedom of a standard Poincaré particle but with a residual set of symmetries that we prove to be BMS. A similar result for the massless limit, including in this case superrotations, is pointed out.

Parametric modeling logic analysis and precision control method application of nonlinear landscape structures based on Rhino+Grasshopper platform: A case study of the Flying Goose viewing platform in Beijing

The development of digital technology has made non-linear landscape structures mainstream and has brought new challenges to design methods. The efficiency and accuracy of applying Rhino+Grasshopper parametric modelling to such structures has gained the attention of design practitioners and scholars. However, there are still research gaps in this approach in current research. Therefore, this study uses the Flying Goose viewing platform as a case study to supplement the lack of specific case studies on non-linear landscape structures; it analyses the modelling logic through three parts: morphological characteristics, structural system, appendages and decoration to supplement the lack of systematic knowledge on modelling logic; it analyses the four methods of unfolding control, isometric projection, function shaping and linear interference. The analysis and discussion of the four core precision control methods used in the Rhino+Grasshopper parametric modelling process complements the current lack of specific research on Rhino+Grasshopper parametric modelling morphological precision control methods. The aim is to provide a systematic analysis of the modelling logic of non-linear landscape structures and a detailed analysis of the precision control methods on top of the non-linear landscape structures morphological realisation, providing a theoretical basis and application examples for future research of the same type.

Nonlinear realization approach to topologically massive supergravity

We develop a nonlinear realization approach to topologically massive supergravity in three dimensions, with and without a cosmological term. It is a natural generalization of a similar construction for N = 1 supergravity in four dimensions, which was recently proposed by one of us. At the heart of both formulations is the nonlinear realization approach to gravity which was given by Volkov and Soroka 50 years ago in the context of spontaneously broken local supersymmetry. In our setting, the action for cosmological topologically massive supergravity is invariant under two different local supersymmetries. One of them acts on the Goldstino, while the other supersymmetry leaves the Goldstino invariant. The former can be used to gauge away the Goldstino, and then the resulting action coincides with that given in the literature.

New dynamical realizations of the Lifshitz group

The method of nonlinear realizations is applied to construct new dynamical realizations of the Lifshitz group in mechanics, hydrodynamics, and field theory.

Ultra-small high‐temperature pressure sensor chips fabricated in single‐layer (111) SOI wafers

This paper presents a 0.5 mm × 0.5 mm tiny-sized high-temperature piezoresistive pressure sensor fabricated with a thin-film under bulk single-sided micromachining process from the front-side of single-layer (111) silicon on insulator (SOI) wafer. The (111)-device layer of the SOI wafer is specifically selected to optimize the piezoresistor performance where the SiO2 buried layer isolates the piezoresistors from the handle substrate. And the (111)-handle layer is employed to subtly construct a single-crystalline-silicon beam-island combining with a very thin but uniform poly-silicon diaphragm for realization of both low nonlinearity and high sensitivity. Without double-sided micromachining process and wafer bonding used, a tiny sensor-chip size of 0.5 mm × 0.5 mm is achieved, which is required in wind-tunnel systems for measuring pressure distribution at high temperature. The testing results of the fabricated sensor show high sensitivity of 0.15 mV V−1 kPa−1 for 150 kPa measure range and satisfactory linearity of ±0.11% FS (full scale) at ambient temperature. At 350 °C, the overall accuracy is 0.17% FS and the thermal hysteresis is 0.22% FS. The temperature coefficient of zero-point offset of the sensor is tested as low as 0.01% °C−1 FS and the temperature coefficient of sensitivity is −0.07% °C−1 FS within the whole temperature range from −55 °C to 350 °C. Featuring the advantages of high accuracy and high-yield low-cost fabrication, the tiny-sized high-temperature pressure sensors exhibit promising perspectives in the field of aerospace industry including wind-tunnel applications.

Performing photonic nonlinear computations by linear operations in a high-dimensional space

Abstract As photonic linear computations are diverse and easy to realize while photonic nonlinear computations are relatively limited and difficult, we propose a novel way to perform photonic nonlinear computations by linear operations in a high-dimensional space, which can achieve many nonlinear functions different from existing optical methods. As a practical application, the arbitrary binary nonlinear computations between two Boolean signals are demonstrated to implement a programmable logic array. In the experiment, by programming the high-dimensional photonic matrix multiplier, we execute fourteen different logic operations with only one fixed nonlinear operation. Then the combined logic functions of half-adder and comparator are demonstrated at 10 Gbit/s. Compared with current methods, the proposed scheme simplifies the devices and the nonlinear operations for programmable logic computing. More importantly, nonlinear realization assisted by space transformation offers a new solution for optical digital computing and enriches the diversity of photonic nonlinear computing.

A non-lorentzian primer

We review both the kinematics and dynamics of non-lorentzian theories and their associated geometries. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras. Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations. We explain the relation with the coadjoint orbit method. We continue discussing three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity. Introducing matter, we discuss electric and magnetic non-lorentzian field theories for three different spins: spin-0, spin-1/2 and spin-1, as limits of relativistic theories.

Inflaton as a pseudo-Nambu-Goldstone boson

In the realistic model of cosmic inflation the inflaton potential should be flat and stable under quantum corrections. It is natural to imagine that there is some symmetry behind and an idea of the inflaton as a Nambu-Goldstone boson of spontaneous breaking of some symmetry has been examined. We give a general formulation of this idea using the non-linear realization of Nambu-Goldstone boson in low-energy effective theory with some explicit symmetry breaking to generate non-trivial potential. The potential is naturally a simple function, typically the mass term of inflaton, and the scenario of “warm inflation” should necessarily be applied under the present observational constraints. We investigate the generation mechanism of necessary thermal dissipation term in inflaton field equation for “warm inflation” without large thermal corrections to inflaton potential. A simple numerical analysis is given to investigate the viability of this scenario.

Local supersymmetry: variations on a theme by Volkov and Soroka

We revisit the work by Volkov and Soroka on spontaneously broken local supersymmetry. It is demonstrated for the first time that, for specially chosen parameters of the theory, the Volkov–Soroka action is invariant under two different local supersymmetries. One of them is present for arbitrary values of the parameters and acts on the Goldstino, while the other supersymmetry emerges only in a special case and leaves the Goldstino invariant. The former can be used to gauge away the Goldstino, and then the resulting action coincides with that proposed by Deser and Zumino for consistent supergravity in the first-order formalism. In this sense, pure N = 1 supergravity is a special case of the Volkov–Soroka theory, although it was not discovered by these authors. We also explain how the Volkov–Soroka approach allows one to naturally arrive at the 1.5 formalism. Our analysis provides a nonlinear realization approach to construct unbroken N = 1 Poincaré supergravity.