Lagrangian Field Research Articles

D-Brane effective Lagrangian in spacetimes with boundaries

AbstractIn this study, we explore the transformation of $$D_p$$ D p -branes to $$D_{p-1}$$ D p - 1 -branes under T-duality when the D-brane is embedded in a spacetime with a boundary. Our goal is to derive the higher-derivative corrections to the Dirac–Born–Infeld (DBI) Lagrangian for both the bulk and boundary terms. For the bulk terms, we calculate the $$\alpha '$$ α ′ corrections for the massless open string fields, up to the 8th order in the dimensionless Maxwell field strength. We demonstrate that the bulk Lagrangian can satisfy the T-duality constraint without residual total derivative terms in the base space. This determines the most general independent couplings of the massless open string fields in the bulk Lagrangian, encompassing 145 coupling constants, up to three parameters. Two of these parameters are physical and are determined by disk-level S-matrix elements, while the third is unphysical and can be eliminated by field redefinitions and integration by parts. The final result for the bulk Lagrangian consists of 49 couplings. For the boundary terms, the application of T-duality symmetry to massless open and closed string fields enables us to extend the DBI Lagrangian to include the boundary unit normal vector field $$n_\mu $$ n μ and its first derivative.

Field theory with the Maxima computer algebra system

The Maxima computer algebra system, the open-source successor to MACSYMA, the first general-purpose computer algebra system that was initially developed at the Massachusetts Institute of Technology in the late 1960s and later distributed by the United States Department of Energy, has some remarkable capabilities, some of which are implemented in the form of add-on, “share” packages that are distributed along with the core Maxima system. One such share package is itensor, for indicial tensor manipulation. One of the more remarkable features of itensor is functional differentiation. Through this, it is possible to use itensor to develop a Lagrangian field theory and derive the corresponding field equations. In this paper, we demonstrate this capability by deriving Maxwell’s equations from the Maxwell Lagrangian, and exploring the properties of the system, including current conservation.

Dissipative quintessential cosmic inflation

In this paper we construct a dissipative quintessential cosmic inflation. For this purpose, we add a multiplicative dissipative term in the standard quintessence field Lagrangian. We consider the specific form of dissipation as the time integral including the Hubble parameter and an arbitrary function that describes the dissipative properties of the quintessential scalar field. Inflation parameters and observables are calculated under slow-roll approximations and a detailed calculation of the cosmological perturbations is performed in this setup. We consider different forms of potentials and calculate the scalar spectral index and tensor-to-scalar ratio for a constant as well as variable dissipation function. To check the reliability of this model, a numerical analysis on the model parameters space is done in confrontation with recent observational data. By comparing the results with observational joint datasets at 68% and 95% confidence levels, we obtain some constraints on the model parameters space, specially the dissipation factor with e-folds numbers N=55 and N=60. As some specific results, we show that the power-law potential with a constant dissipation factor and N=60 is mildly consistent with observational data in some restricted domains of the model parameter space with very small and negative dissipation factor and a negligible tensor-to-scalar ratio. But this case with N=55 is consistent with observation considerably. For power-law potential and variable dissipation factor as Q=αϕn, the consistency with observation is also considerable with a reliable tensor-to-scalar ratio. The quadratic and quartic potentials with variable dissipation function as Q=αϕn are consistent with Planck2018 TT, TE, EE+lowE+lensing data at the 68% and 95% levels of confidence for some intervals of the parameter n.

Phase-space analysis in non-minimal symmetric-teleparallel dark energy

We modify the symmetric-teleparallel dark energy through the addition of a further Yukawa-like term, in which the non-metricity scalar, Q, is non-minimally coupled to a scalar field Lagrangian where the phion acts as quintessence, describing dark energy. We investigate regions of stability and find late-time attractors. To do so, we conduct a stability analysis for different types of physical potentials describing dark energy, namely the power-law, inverse power-law, and exponential potentials. Within these choices, we furthermore single out particular limiting cases, such as the constant, linear and inverse potentials. For all the considered scenarios, regions of stability are calculated in terms of the signs of the coupling constant and the exponent, revealing a clear degeneracy among coefficients necessary to ensure stability. We find that a generic power-law potential with α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document} is not suitable as a non-minimal quintessence potential and we put severe limits on the use of inverse potential, as well. In addition, the equations of state of each potential have been also computed. We find the constant potential seems to be favored than other treatments, since the critical point appears independent of the non-minimal coupling.

On the entropy inequality and its exploitation in continuum physics

AbstractThe paper deals with the statement and the application of the entropy principle, through the Clausius–Duhem inequality, in continuum physics. The conceptual role is taken from the Coleman–Noll paper of 1963 thus leading to the physical admissibility of constitutive equations. The statement is generalized by letting the rate of entropy production be a constitutive property per se. This generalization proves essential in connection with the modelling of hysteretic phenomena. As to the application, the view of the Coleman–Noll procedure is maintained but a representation formula is shown to generalize the consequences of the entropy principle; as an example the modelling of heat conduction is investigated. Furthermore, while applying the entropy principle to magnetic materials, it is shown an interesting connection between the balance of angular momentum and the thermodynamic restrictions. Also, the modelling through rate-type equations shows the need of Lagrangian fields to obey objectivity and that of the entropy production as a constitutive function to account for the difference between loading and unloading processes.

Wormholes inside stars and black holes

We construct models of two exotic objects: (i) a wormhole whose throat is hidden by a stellar object like a neutron star; and (ii) a wormhole inside a black hole. We work within Einstein’s gravity coupled to two scalar fields with a specific choice of the scalar field Lagrangian. In general, the model contains ghosts, but they are eliminated using the constraints given by the Lagrange multiplier fields. The constraints are a generalization of the mimetic constraint, where nondynamical dark matter effectively appears. As a result, in our model, instead of the nondynamical dark matter, nondynamical exotic matter like a phantom effectively arises. For the mixed wormhole-plus-star system, we find the corresponding mass-radius relation and show that it is possible to get characteristics comparable to those of ordinary neutron stars. For the wormhole inside the black hole, we find an extremal limit where the radius of the throat coincides with the radius of the event horizon and demonstrate that the Hawking temperature vanishes in this limit. Published by the American Physical Society 2024

EFTofLSS meets simulation-based inference: σ 8 from biased tracers

Cosmological inferences typically rely on explicit expressions for the likelihood and covariance of the data vector, which normally consists of a set of summary statistics. However, in the case of nonlinear large-scale structure, exact expressions for either likelihood or covariance are unknown, and even approximate expressions can become very cumbersome, depending on the scales and summary statistics considered. Simulation-based inference (SBI), in contrast, does not require an explicit form for the likelihood but only a prior and a simulator, thereby naturally circumventing these issues. In this paper, we explore how this technique can be used to infer σ 8 from a Lagrangian effective field theory (EFT) based forward model for biased tracers. The power spectrum and bispectrum are used as summary statistics to obtain the posterior of the cosmological, bias and noise parameters via neural density estimation. We compare full simulation-based inference with cases where the data vector is drawn from a Gaussian likelihood with sample and analytical covariances. We conclude that, for k max = 0.1hMpc-1 and 0.2hMpc-1, the form of the covariance is more important than the non-Gaussianity of the likelihood, although this conclusion is expected to depend on the cosmological parameter inferred, the summary statistics considered and range of scales probed.

Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws

It is well known that [Formula: see text]-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the [Formula: see text]-contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the [Formula: see text]-contact Euler–Lagrange equations written in terms of [Formula: see text]-vector fields and sections and provide new results relating the solutions in both approaches. We also study different kinds of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and [Formula: see text]-contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyze the relation between [Formula: see text]-contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example.

Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative U(1) gauge theory

This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether’s theorem tailored for nonlocal Lagrangians. Finally, we apply both the formalism and the extended theorem to the context of non-commutative U(1) gauge theory, including its Hamiltonian and quantization, showcasing their practical utility.

Three-dimensional time-resolved Lagrangian flow field reconstruction based on constrained least squares and stable radial basis function

Three-dimensional time-resolved Lagrangian flow field reconstruction based on constrained least squares and stable radial basis function

The field theory of collective Cherenkov radiation associated with electron beams

Classical Cherenkov radiation is a celebrated physics phenomenon of electromagnetic (EM) radiation stimulated by an electric charge moving with constant velocity in a three-dimensional dielectric medium. Cherenkov radiation has a wide spectrum and a particular distribution in space similar to the Mach cone created by a supersonic source. It is also characterized by the energy transfer from the charge's kinetic energy to the EM radiation. In the case of an electron beam passing through the middle of an EM waveguide, the radiation is manifested as collective Cherenkov radiation. In this case, the electron beam can be viewed as a one-dimensional non-neutral plasma, whereas the waveguide can be viewed as a slow wave structure. This collective radiation occurs, in particular, in traveling wave tubes (TWTs), and it features the energy transfer from the electron beam to the EM radiation in the waveguide. Based on a first principles Lagrangian field theory, we develop a convincing argument that the collective Cherenkov effect in TWTs is, in fact, a convective instability, that is, amplification. We also recover Pierce's theory as a high-frequency limit of our generalized Lagrangian theory. Finally, we derive for the first time expressions identifying low- and high-frequency cutoffs for amplification in TWTs.

Constraint characterization and degree of freedom counting in Lagrangian field theory

Constraint characterization and degree of freedom counting in Lagrangian field theory

Field theory description of the non-perturbative optical nonlinearity of epsilon-near-zero media

In this paper, we introduce a fully non-perturbative approach for the description of the optical nonlinearity of epsilon-near-zero (ENZ) media. In particular, based on the rigorous Feynman path integral method, we develop a dressed Lagrangian field theory for light–matter interactions and discuss its application to dispersive Kerr-like media with order-of-unity light-induced refractive index variations. Specifically, considering the relevant case of Indium Tin Oxide (ITO) nonlinearities, we address the novel regime of non-perturbative refractive index variations in ENZ media and establish that it follows naturally from a scalar field theory with a Born–Infeld Lagrangian. Moreover, we developed a predictive model that includes the intrinsic saturation effects originating from the light-induced modification of the Drude terms in the linear dispersion of ITO materials. Our results extend the Huttner–Barnett–Bechler electrodynamics model to the case of non-perturbative optical Kerr-like media providing an intrinsically nonlinear, field-theoretic framework for understanding the exceptional nonlinearity of ITO materials beyond traditional perturbation theory.

Deriving the cosmological constant from the Euler–Lagrange equation of second-order differentiable gravitational field Lagrangian

The principles underlying the variational approach prove to be invaluable tools in articulating physical phenomena, particularly when dealing with conserved quantities. The derivation of gravitational field equations from the Euler–Lagrange equation, a result of the first-order derivative of Lagrange field density, is a well-established concept. However, within the context of this paper, the field equations stem from the second-order differentiable field Lagrangian in the Euler–Lagrange equation. The Euler–Lagrange equation of the first-order differentiable field Lagrangian yields the gravitational field equations incorporating matter fields and the cosmological constant. On the other hand, the Euler–Lagrange equation of the second-order differentiable field Lagrangian gives rise to the equation governing the cosmological constant. The procedure of determining the cosmological constant through the Euler–Lagrange equation adheres to fundamental mathematical theory encompassing higher-order Euler–Lagrange equations. This theory implies that utilizing higher-order Euler–Lagrange equations may result in instability due to negative energy. The cosmological constant is postulated to be intertwined with negative vacuum energy density. The value assigned to the gravitational constant, as ascertained through the employment of the general relativistic equation, is not only significantly small and nonzero but also demonstrates remarkable compatibility with the value inferred from observational deductions.

Consistent Lagrangians for Irreducible Interacting Higher-Spin Fields with Holonomic Constraints

Consistent Lagrangians for Irreducible Interacting Higher-Spin Fields with Holonomic Constraints

Generalization of Noether Theorem and action principle for non-Lagrangian theories

A non-Lagrangian field theory is a theory whose field equations cannot be derived from the action principle. The action principle is described by holonomic variational equations. These equations can be used only for standard field theories, equations of which can be represented as Euler–Lagrange equations for some Lagrangian density. In the general case, one should use non-holonomic variational equations to obtain a wider class of field equations. In this paper, it is proposed to use the Sedov non-holonomic variational equation as a generalization of action principle. Examples of application of non-holonomic variational equations to derive various field equations are suggested. The standard Noether theorem is formulated for the standard (Lagrangian) field theory with an action functional and expresses the invariance of the Lagrangian with respect to some continuous group of transformations. In this paper, a generalization of Noether’s theorem for non-Lagrangian field theories is proposed and proved by using the non-holonomic variational equation. The expression of Noether current is described in the general case of non-Lagrangian field theory. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory. An important result of this paper is the proof of possibility of existence of some analogues of dissipative structures in non-Lagrangian field theories and some properties of such structures are suggested.

SequenceMorph: A Unified Unsupervised Learning Framework for Motion Tracking on Cardiac Image Sequences.

Modern medical imaging techniques, such as ultrasound (US) and cardiac magnetic resonance (MR) imaging, have enabled the evaluation of myocardial deformation directly from an image sequence. While many traditional cardiac motion tracking methods have been developed for the automated estimation of the myocardial wall deformation, they are not widely used in clinical diagnosis, due to their lack of accuracy and efficiency. In this paper, we propose a novel deep learning-based fully unsupervised method, SequenceMorph, for in vivo motion tracking in cardiac image sequences. In our method, we introduce the concept of motion decomposition and recomposition. We first estimate the inter-frame (INF) motion field between any two consecutive frames, by a bi-directional generative diffeomorphic registration neural network. Using this result, we then estimate the Lagrangian motion field between the reference frame and any other frame, through a differentiable composition layer. Our framework can be extended to incorporate another registration network, to further reduce the accumulated errors introduced in the INF motion tracking step, and to refine the Lagrangian motion estimation. By utilizing temporal information to perform reasonable estimations of spatio-temporal motion fields, this novel method provides a useful solution for image sequence motion tracking. Our method has been applied to US (echocardiographic) and cardiac MR (untagged and tagged cine) image sequences; the results show that SequenceMorph is significantly superior to conventional motion tracking methods, in terms of the cardiac motion tracking accuracy and inference efficiency.

Study of the scalar-fermionic model containing linear lagrangian fields of matter within the framework of minimal coupling

In this article, we study a model of the universe with the scalar field and the fermionic field interacting via a Yukawa-type potential. In the model, the component contributions of each of the fields are determined to the total density and pressure of dark energy. We have considered the solution of the cosmological model for the scale factor with two functional time dependences. The Yukawa-type field does not give its input to the general pressure. In the power law case, there is a significant contribution to the total increase in pressure, to the exponential — the scalar field. There are many cases when the universe makes a transition between successive epochs in various models of cosmological expansion. These regularities impose some restrictions on the profile of the scalar- fermionic field interaction and the general cosmological dynamics. Energy conditions were found to check the model under the study. In the studied model, the null energy condition, the strong energy condition, the dominant energy condition are fulfilled, and the weak energy condition, which is not mandatory, is not fulfilled. It is shown how it is possible to connect the cosmographic parameters — parameters of deceleration q, jerk j and snap s with the power low the scale factor. We investigated these restrictions using cosmological solutions with an evolving equation of state, such that a smooth transition between different epochs can always occur in the universe. The scalar-fermionic model under study describes the accelerated modes of expansion of the universe. The obtained solutions correspond to the results predicted by the theory and observational data.

Energy–momentum tensor: Noether vs Hilbert

Several definitions of the energy–momentum tensor in classical field models on differential manifolds are examined in this work. We specifically talk about the connection between - Hilbert’s symmetric and Noether’s asymmetric energy–momentum tensors. We consider a matter field Lagrangian on a manifold endowed with a teleparallel (coframe) structure. The associated 3-form of coframe conserved current can be viewed as a link between Noether’s and Hilbert’s energy–momentum tensors. In these circumstances, we are able to show the complete equivalence of Hilbert’s and Noether’s currents for the matter field.

Lagrangian displacement field estimators in cosmology

The late-time nonlinear Lagrangian displacement field is highly correlated with the initial field, so reconstructing it could enable us to extract primordial cosmological information. Our previous work [A. Ota et al., Phys. Rev. D 104, 123508 (2021)] carefully studied the displacement field reconstructed from the late-time density field using the iterative method proposed by Schmittfull et al. [Phys. Rev. D 96, 023505 (2017)] and found that it does not fully converge to the true, underlying displacement field (e.g., $\ensuremath{\sim}8%$ offset at $k\ensuremath{\sim}0.2\text{ }\text{ }h\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ at $z=0.6$). We also constructed the Lagrangian perturbation theory model for the reconstructed field, but the model could not explain the discrepancy between the true and the reconstructed fields in the previous work. The main sources of the discrepancy were speculated to be a numerical artifact in the displacement estimator due to the discreteness of the sample. In this paper, we develop two new estimators of the displacement fields to reduce such a numerical discreteness effect, the normalized momentum estimator and the rescaled resumed estimator. We show that the discrepancy Ota et al. [Phys. Rev. D 104, 123508 (2021)] reported is not due to the numerical artifacts. We conclude that the method from Schmittfull et al. [Phys. Rev. D 96, 023505 (2017)] cannot fully reconstruct the shape of the nonlinear displacement field at the redshift we studied, while it is still an efficient baryon acoustic oscillation reconstruction method. In parallel, by properly accounting for the UV-sensitive term in a reconstruction procedure with an effective field theory approach, we improve the theoretical model for the reconstructed displacement field, by almost 5 times, from $\ensuremath{\sim}15%$ to the level of a few percent at $k\ensuremath{\sim}0.2\text{ }\text{ }h\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ at the redshift $z=0.6$.