Field In Spacetime Research Articles

Orientation selectivity properties for the affine Gaussian derivative and the affine Gabor models for visual receptive fields.

This paper presents an in-depth theoretical analysis of the orientation selectivity properties of simple cells and complex cells, that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation. A detailed mathematical analysis is presented for the three different cases of either: (i) purely spatial receptive fields, (ii) space-time separable spatio-temporal receptive fields and (iii) velocity-adapted spatio-temporal receptive fields. Closed-form theoretical expressions for the orientation selectivity curves for idealized models of simple and complex cells are derived for all these main cases, and it is shown that the orientation selectivity of the receptive fields becomes more narrow, as a scale parameter ratio , defined as the ratio between the scale parameters in the directions perpendicular to vs. parallel with the preferred orientation of the receptive field, increases. It is also shown that the orientation selectivity becomes more narrow with increasing order of spatial differentiation in the underlying affine Gaussian derivative operators over the spatial domain. A corresponding theoretical orientation selectivity analysis is also presented for purely spatial receptive fields according to an affine Gabor model, showing that: (i)the orientation selectivity becomes more narrow when making the receptive fields wider in the direction perpendicular to the preferred orientation of the receptive field; while (ii)an additional degree of freedom in the affine Gabor model does, however, also strongly affect the orientation selectivity properties.

Fermionic entanglement in the presence of background electric and magnetic fields

In this study, we investigate the fermionic Schwinger effect in the presence of a constant magnetic field within (1+3)-dimensional Minkowski spacetime, considering both constant and pulsed electric fields. We analyze the correlations between Schwinger pairs for the vacuum and maximally entangled states of two fermionic fields. The correlations are quantified using entanglement entropy and Bell’s inequality violation for the vacuum state, while Bell’s inequality violation and mutual information are used for the maximally entangled state. One can observe the variation of the entanglement produced for fermionic modes with respect to different parameters. Additionally, we discuss the key differences from the behaviour of scalar fields in this context. This study offers deeper insights into quantum field theory and the dynamics of entanglement in the fermionic Schwinger effect.

Geodesics in Carrollian Reissner-Nordström black holes

In this work, we study the geodesics in different Carrollian limits of RN (Reissner-Nordström) black holes, considering the motions of both neutral and charged particles. We use the geodesic equations in the weak Carrollian structure and analyze the corresponding trajectories projected onto the absolute space, and find that the geodesics are well defined. In particular, we examine the electric-electric and magnetic-electric limit of the RN black hole, focusing on their geodesic structures. We find that the global structures of the usual RN black holes get squeezed under the ultrarelativistic limit. More precisely, the nonextreme magnetic-electric RN spacetime has two different asymptotic flat patches while the extreme black hole spacetime consists of only one patch. For the magnetic-electric RN spacetime, the Carrollian extremal surfaces (CESs) divide the spacetime into several geodesically complete regions, and the geodesics can only travel in one of these regions. For the charged particles, we extend the analysis by considering their interactions with the electromagnetic field in the Carrollian RN spacetimes and find that their trajectories are significantly different from the neutral geodesics. Published by the American Physical Society 2024

O(rN) two-form asymptotic symmetries and renormalized charges

We investigate O(rN) asymptotic symmetries for a two-form gauge field in four-dimensional Minkowski spacetime. By employing symplectic renormalization, we identify N independent asymptotic charges, with each charge being parametrised by an arbitrary function of the angular variables. Working in Lorenz gauge, the gauge parameters require a radial expansion involving logarithmic (subleading) terms to ensure nontrivial angular dependence at leading order. At the same time, we adopt a setup where the field strength admits a power expansion, allowing logarithms in the gauge field expansions within pure gauge sectors. The same setup is studied for electromagnetism.

A numerical solution of Schrödinger equation for the dynamics of early universe

Artificial neural networks (ANNs) have attained widespread success across varied disciplines. This study is designated for looking into an application of an integrated intelligent computing paradigm concerning dynamics in the early Universe through numerical solutions to the Schrödinger equation. To arrive at this we leverage the Levenberg–Marquardt backpropagation networks (LMBNs) to probe cosmic evolution in the early Universe with the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric for a flat minisuperspace model of the Universe in the background. This leads to bridging quantum mechanics and inflationary Universe dynamics conducing to quantum cosmology within the standard model. Wheeler–DeWitt equation corresponds to the time-independent Schrödinger equation obtained from the equations of motion for a single scalar field in flat spacetime with FLRW metric. Utilizing the ntstool the whole computing process is operated for simulation. To evaluate the accuracy and efficiency of the proposed scheme a comparative analysis is carried out. To construct continuous neural network mappings we employ the explicit Runge–Kutta method as the target parameter for generating datasets. To determine the solution datasets of different scenarios, the training, testing, and validation processes are employed to take advantage of these in the learning of neural network models established upon the backpropagation technique of Levenberg–Marquardt. By varying related parameters we develop three scenarios that produce nine cases, three for each. The data plots of performance, training state, error histogram, regression, time-series response, and error autocorrelation represent the visualization of the results. These plots show a complete case description by displaying all the necessary data values. The analysis of these plots is presented to validate all the cases. Performing the analysis by mean square error (MSE) validates the achieved accuracy of the results by validating and verifying neural networks. This work is motivated by the compelling need to develop innovative computational methods for solving complex cosmological questions to untangle the conundrums of the early universe. The attractive numerical solutions of the Schrödinger equation for the early Universe heralds a step towards quantum cosmology based on the interplay of the Wheeler–DeWitt equation and time-independent Schrödinger equation. There is an increasing trend to use computational methods to solve ordinary and partial differential equations with the help of code development in Matlab. For this purpose feed-forward artificial neural network is used for investigating the Schrödinger equation.

Kerr black hole mimickers sourced by a string fluid

We present rotating solutions of Einstein's gravity coupled to an effective Born-Infeld theory that describes the end of open-string tachyon condensation after the decay of an unstable D-brane or a brane-antibrane system. The geometry of these solutions is that of the rotating frozen star. The solutions are stationary, ultracompact, can be made non-singular via a regularization procedure and their exterior geometry is identical, for all practical purposes, to that of the Kerr solution. The Born-Infeld matter consists of radial electric-flux tubes that emanate from, or end at, the ellipsoidal core of the star. Each end of the flux tubes carries an electric charge, so that the electric field can be viewed as being sourced by an ellipsoidal charge distribution of positive and negative charges near the center of the star. Meanwhile, the star's outer layer is equal and oppositely charged, resulting in a vanishing electric field in the external spacetime. We show that these rotating solutions are ultrastable against radial perturbations, just like their static frozen star counterparts. They are also effectively immune to ergoregion instabilities, as we discuss.

Perturbation of spacetime and electromagnetic field due to massive charged particle around electrically charged stringy black hole

Perturbation of spacetime and electromagnetic field due to massive charged particle around electrically charged stringy black hole

Momentum spectrum of nonlinear Breit-Wheeler pair production in spacetime fields

We show how to use a worldline-instanton formalism to calculate, to leading order in the weak-field expansion, the momentum spectrum of nonlinear Breit-Wheeler pair production in fields that depend on time and one spatial coordinate. We find a nontrivial dependence on the width, λ, of the photon wave packet, and the existence of a critical point λc. For λ<λc and a field with one peak, the spectrum has one peak where the electron and positron have the same energy. For λ>λc this splits into two peaks. We calculate a high-energy (Ω≫1) expansion, which to leading order agrees with the results obtained by replacing the spacetime field with a plane wave and using the well-known Volkov solutions. We also calculate an expansion for Ω∼a0≫1, where the field is strong enough to significantly bend the trajectories of the fermions despite Ω≫1. Published by the American Physical Society 2024

Connections between kinks with different asymptotics

In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional space-time. We show how to obtain new models with solitons having different asymptotic behavior, using deformations with specific functions. In particular, starting from the well-known model, we obtain kinks with super-exponential, super-super-exponential, power-law, and logarithmic asymptotics. We also comment on how asymptotic behavior of stability potential and zero mode can be obtained for deformed kinks.

Bosonic and fermionic coherence of N-partite states in the background of a dilaton black hole

We study the N-partite coherences of GHZ and W states for free bosonic and fermionic fields when any n observers hover near the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. We derive the more general analytical expressions for N-partite coherence, encompassing both physically accessible and inaccessible coherences in the context of the dilaton black hole. It has been found that the coherence of the bosonic field is greater than that of the fermionic field, while the entanglement of the fermionic field is greater than that of the bosonic field in dilaton spacetime. Additionally, the coherence of the W state is greater than that of the GHZ state, whereas the entanglement of the GHZ state is greater than that of the W state in curved spacetime. These results suggest that we should utilize suitable quantum resources and different types of particles for relativistic quantum information tasks.

Estimation of average differential entropy for a stationary ergodic space-time random field on a bounded area

Estimation of average differential entropy for a stationary ergodic space-time random field on a bounded area

Loop correction and resummation of vertex functions for a self interacting scalar field in the de Sitter spacetime

We consider a massless and minimally coupled self interacting quantum scalar field theory in the inflationary de Sitter background of dimension four. The self interaction potential is taken to be either quartic, λϕ4/4!, or quartic plus cubic, λϕ4/4!+βϕ3/3! (λ>0). We compute the four and three point vertex functions up to two loop. The purely local or partly local part of these renormalised loop corrected vertex functions grow unboundedly after sufficient number of de Sitter e-foldings, due to the appearances of secular logarithms. We focus on the purely local part of the vertex functions and attempt a resummation of them in terms of the dynamically generated mass of the scalar field at late times. Such local logarithms have sub-leading powers compared to the non-local leading ones which can be resummed via the stochastic formalism. The variation of these vertex functions are investigated with respect to the tree level couplings numerically. Since neither the secular effect, nor the dynamical generation of field mass is possible in the Minkowski spacetime, the above phenomenon has no flat spacetime analogue. We have also compared our result with the ones that could be found via the recently proposed renormalisation group techniques. All these results suggest that at late times the value of the non-perturbative vertex function should be less than the tree level coupling.

Stability of lower dimensional counter-rotating thin-shell wormholes with scalar hair

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes.

CFT reconstruction of local bulk operators in half-Minkowski space

We construct a holographic map that reconstructs massless fields (scalars, Maxwell field, and Fierz-Pauli field) in half-Minkowski spacetime in d+1 dimensions terms of smeared primary operators in a large-N factorizable CFT in Rd−1,1. This map is based on a Weyl (rescaling) transformation from the Poincaré wedge of AdS to the Minkowski half-space and on the Hamilton-Kabat-Lifschytz-Lowe smearing function, which reconstructs local bulk operators in the Poincaré AdS in terms of smeared operators on the conformal boundary of the Poincaré wedge. The massless scalar field is reconstructed up to the level of two-point functions, while the Maxwell field and massless spin-2 fields are reconstructed at the level of the one-point function. We also discuss potential ways the map can be generalized to higher dimensions, and to the full Minkowski space. Published by the American Physical Society 2024

Faddeev–Jackiw Hamiltonian formulation for general exotic bi-gravity

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants βn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{n}$$\\end{document} and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

Kodama-like vector fields in axisymmetric spacetimes

We extend the concept of the Kodama symmetry, a quasi-local time translation symmetry for dynamical spherically symmetric spacetimes, to a specific class of dynamical axisymmetric spacetimes, namely the families of Kerr–Vaidya and Kerr–Vaidya–de Sitter spacetimes. We study some geometrical properties of the asymptotically flat Kerr–Vaidya metric, such as the Brown–York mass and the Einstein tensor. Furthermore, we propose a generalization of the Kerr–Vaidya metric to an asymptotic de Sitter background. We show that for these classes of dynamical axisymmetric black hole spacetimes, there exists a timelike vector field that exhibits similar properties to the Kodama vector field in spherical symmetry. This includes the construction of a covariantly conserved current and a corresponding locally conserved charge, which in the Kerr–Vaidya case converges to the Brown–York mass in the asymptotically flat region.

Entanglement harvesting in cosmic string spacetime

We investigate the entanglement harvesting phenomenon for static detectors that locally interact with massless scalar fields in the cosmic string spacetime, which, though locally flat, features a conical structure defined by a deficit angle. Specifically, we analyze three detector alignments relative to the string: parallel and orthogonal alignments with detectors on the same side of the string, and an orthogonal alignment with detectors on opposite sides of the string. For the alignments on the same side of the string, we observe that the cosmic string’s presence can either aid or hinder entanglement harvesting, affecting both the extent of entanglement harvested and the achievable range of interdetector separation. This effect depends on the distance between the detectors and the string and differs markedly from scenarios in a locally flat spacetime with a reflecting boundary, where the boundary invariably extends the harvesting-achievable range. Conversely, for the alignment with detectors on opposite sides of the string, we find that detectors consistently harvest more entanglement than those in a flat spacetime devoid of a cosmic string. This starkly contrasts the behavior observed with detectors on the same side. Interestingly, the presence of a cosmic string expands the harvesting-achievable range for detectors in orthogonal alignment only when near the string, whereas it invariably reduces the achievable range for detectors in parallel alignment.

A Variational Surface-Evolution Approach to Optimal Transport over Transitioning Compact Supports with Domain Constraints

We examine the optimal mass transport problem in Rn between densities with transitioning compact support by considering the geometry of a continuous interpolating support boundary Γ in space-time within which the mass density evolves according to the fluid dynamical framework of Benamou and Brenier. We treat the geometry of this space-time embedding in terms of points, vectors, and sets in Rn+1=R×Rn and blend the mass density and velocity as well into a space-time solenoidal vector field W|Ω→Rn+1 over a compact set Ω⊂Rn+1. We then formulate a joint optimization for W and its support using the shaped gradient of the space-time surface Γ outlining the support boundary ∂Ω. This easily accommodates spatiotemporal constraints, including obstacles or mandatory regions to visit.

Quantum approach to bound states in field theory

It is well known that (possibly nonunique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In [R. M. Wald, ], Wald derived a conserved energy functional for each prescribed dynamics. This conserved energy is related to the positive self-adjoint extensions of the spatial part A of the wave equation ∂2Φ/∂t2=−AΦ (A may not be, in principle, essentially self-adjoint). This is quite surprising since the canonical energy is not conserved in these cases. In this paper, we rederive this energy functional from an action principle (with appropriate boundary terms) following [A. A. Saharian, ] and consider field dynamics arising from nonpositive self-adjoint extensions of A. The spectrum of the resulting theory fails to be positive and unstable mode solutions for classical fields come to light. By studying fields in half-Minkowski spacetime, we illustrate that these unstable classical solutions come as a consequence of an inverted parabolic potential governing their dynamics. From the quantum mechanical point of view, this leads to an effective inverted harmonic oscillator at the boundary. We then explore these unstable modes behavior, as well as their instabilities, at the quantum level. Published by the American Physical Society 2024

Quasinormal modes and bound states of massive scalar fields in wormhole spacetimes

Quasinormal modes and bound states of massive scalar fields in wormhole spacetimes