Spinor Fields Research Articles

A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model

On a d-dimensional Riemannian, spin manifold (M, g) we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in Dappiaggi et al (Commun Contemp Math 27(07):2150075, 2022), for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if d≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 2$$\\end{document}.

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Loops in AdS: from the spectral representation to position space. Part III

We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-Nf conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in 1Nf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N_f} $$\\end{document}. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as “blob diagrams”. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a k-loop ladder diagram.

Enhanced multifunctional sensing in human motion with speed-controlled coaxial wet-spun hollow MWCNT-TPU/TPU smart fibers

In the field of personal health management and athletic performance optimization, the demand for multi-parameter human signal monitoring devices is rapidly increasing. Currently, flexible sensors produced through wet spinning techniques face challenges of simplistic structure and functionality, as well as difficulty in balancing strength and sensitivity. In-depth research is needed to develop high-performance wet spinning techniques, which will lay the foundation for commercial smart garments capable of unobtrusively monitoring human motion in the future. This study innovatively employs specialized slurry formulations and spinning speed controls to utilize the timing differences in fiber precipitation and the affinity among similar materials. Through the coaxial wet spinning process, it enables the continuous, large-scale manufacturing of hollow core–shell fibers, MT/T-S5, which feature a dense inner layer and a porous outer conductive layer. This special structure endows the fibers with high strength, high signal stability, and capabilities for both active and passive heating. These fibers achieve a maximum gauge factor (GF) 65.2 in stretch sensing applications and can detect pressures as low as 0.1 N. The MT/T-S5 smart fibers can sense human joint movements, and through connection with an Arduino microcontroller, they can control a robotic hand and perform independent and real-time motion detection of five fingers to distinguish gestures. This research not only provides a new type of fiber material for the development of future smart textiles but also reveals a formation mechanism for hollow core–shell fibers in the field of wet spinning. This discovery can offer valuable inspiration for fiber structural design in future research.

Unconventional conformal invariance of maximal depth partially massless fields on dS4 and its relation to complex partially massless SUSY

Deser and Waldron have shown that maximal depth partially massless theories of higher (integer) spin on four-dimensional de Sitter spacetime (dS4) possess infinitesimal symmetries generated by the conformal Killing vectors of dS4. However, it was later shown by Barnich, Bekaert, and Grigoriev that these theories are not invariant under the conformal algebra so(2, 4). To get some insight into these seemingly contradicting results we write down the full set of infinitesimal transformations of the fields generated by the fifteen conformal Killing vectors of dS4. In particular, although the infinitesimal transformations generated by the ten dS Killing vectors are well-known (these correspond to the conventional Lie derivatives), the transformations generated by the five non-Killing conformal Killing vectors were absent from the literature, and we show that they have an ‘unconventional’ form. In the spin-2 case (partially massless graviton), we show that the field equations and the action are invariant under the unconventional conformal transformations. For spin s > 2, the invariance is demonstrated only at the level of the field equations. For all spins s ≥ 2, we reproduce the result that the symmetry algebra does not close on the conformal algebra, so(2, 4). This is due to the appearance of new higher-derivative symmetry transformations in the commutator of two unconventional conformal transformations. Our results concerning the closure of the full symmetry algebra are inconclusive. Then we shift focus to the question of supersymmetry (SUSY) on dS4 and our objective is twofold. First, we uncover a non-interacting supermultiplet that consists of a complex partially massless spin-2 field and a complex spin-3/2 field on dS4. Second, we showcase the appearance of the unconventional conformal symmetries in the commutator of two SUSY transformations. Thus, this commutator closes on an algebra that is neither so(1, 4) nor so(2, 4), while its full structure is an open question. More open questions arising from our findings are also discussed.

Lorentz-violating extension of Wigner function formalism and chiral kinetic theory

The quantum kinetic equation for the gauge-invariant Wigner function, constructed from spinor fields that obey the Dirac equation modified by CPT and Lorentz symmetry-violating terms, is presented. The equations for the components of the Wigner function in the Clifford algebra basis are accomplished. Focusing on the massless case, an extended semiclassical chiral kinetic theory in the presence of external electromagnetic fields is developed. We calculate the chiral currents and establish the anomalous magnetic and separation effects in a Lorentz-violating background. The chiral anomaly within the context of extended quantum electrodynamics is elucidated. Finally, we derive the semiclassical Lorentz-violating extended chiral transport equation. Published by the American Physical Society 2024

Lorentz violating backgrounds from quadratic, shift-symmetric, ultralight dark matter

We consider an effective theory for a shift-symmetric, quadratically-coupled, ultralight spin-0 field. The leading CP conserving interactions with Standard Model fields in the effective theory arise at dimension 8. We discuss the renormalization group evolution and positivity bounds on these operators, as well as their possible UV origins. Assuming that the spin-0 field is associated with an ultralight dark matter candidate, we discuss the effects of the dimension-8 operators on experiments searching for the oscillation of fundamental constants and Lorentz violation. We find that the direct bounds on these two effects are of similar strength but rather weak, corresponding to a UV cutoff scale of keV order, as they are mediated by dimension-8 operators.

Logarithmic correlation functions in 2D critical percolation

It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation.

Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension D>4, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In D=4, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in D=4, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in the xy plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription associated with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures. Published by the American Physical Society 2024

The renormalization group for large-scale structure: primordial non-Gaussianities

The renormalization group for large-scale structure (RG-LSS) describes the evolution of galaxy bias and stochastic parameters as a function of the cutoff Λ. In this work, we introduce interaction vertices that describe primordial non-Gaussianity into the Wilson-Polchinski framework, thereby extending the free theory to the interacting case.The presence of these interactions forces us to include new operators and bias coefficients to the bias expansion to ensure closure under renormalization.We recover the previously-derived “scale-dependent bias” contributions, as well as a new (subdominant) stochastic contribution.We derive the renormalization group equations governing the RG-LSS for a large class of interactions which account for vertices at linear order in f NL that parametrize interacting scalar and massive spinning fields during inflation.Solving the RG equations, we show the evolution of the non-Gaussian contributions to galaxy clustering as a function of scale.

Momentum-space formulae for AdS correlators for diverse theories in diverse dimensions

In this paper, we explore correlators of a series of theories in anti-de Sitter space: we present comprehensive results for interactions involving scalars, gluons, and gravitons in multiple dimensions. One aspect of our investigation is the establishment of an intriguing connection between the kinematic factors of these theories; indeed, such a connection directly relates these theories among themselves and with other theories of higher spin fields. Besides providing several explicit results throughout the paper, we also highlight the interconnections and relationships between these different theories, providing valuable insights into their similarities and distinctions.

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

κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-Dirac stars

In this paper, we construct a Dirac star model composed of |κ|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |$$\\end{document} pairs of spinor fields. The azimuthal harmonic indices m of these spinor fields are half-integers, and they satisfy -(|κ|-12)≤m≤|κ|-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-(|\\kappa |-\\frac{1}{2})\\le m \\le |\\kappa |-\\frac{1}{2}$$\\end{document}. When κ=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa =1$$\\end{document}, it corresponds to the conventional Dirac star model, formed by two spinor fields with m=12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=\\frac{1}{2}$$\\end{document} and m=-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=-\\frac{1}{2}$$\\end{document}. When |κ|>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |>1$$\\end{document}, among these |κ|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |$$\\end{document} pairs of spinor fields, there exist spinor fields with azimuthal harmonic indices m>12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m>\\frac{1}{2}$$\\end{document}, and all spinor fields still conform to the same Dirac field equation. Different families of solutions are distinguished by the value of κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, so we named these solutions κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-Dirac stars. We obtain solutions for κ=±1,±2,±3,±4,±5,±6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa =\\pm 1,\\pm 2,\\pm 3,\\pm 4,\\pm 5,\\pm 6$$\\end{document} by using numerical methods. Additionally, we compute their ADM mass M, Noether charge Q, and binding energy E, and illustrate how these quantities change with the spinor field’s frequency ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} for different κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}. We observe significant differences between solutions for |κ|>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |>1$$\\end{document} and the |κ|=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |=1$$\\end{document} case. Furthermore, we provide the energy density distribution of the Dirac stars, wherein for |κ|>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\kappa |>1$$\\end{document} scenarios, the Dirac stars exhibit a spherical shell-like structure. Moreover, we employ three-dimensional diagrams to intuitively depict how κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} influences the combination of spinor fields to form a spherically symmetric configuration.

Suppressing Thermal Noise to Sub-Millikelvin Level in a Single-Spin Quantum System Using Realtime Frequency Tracking.

A single nitrogen-vacancy (NV) center in a diamond can be used as a nanoscale sensor for magnetic field, electric field or nuclear spins. Due to its low photon detection efficiency, such sensing processes often take a long time, suffering from an electron spin resonance (ESR) frequency fluctuation induced by the time-varying thermal perturbations noise. Thus, suppressing the thermal noise is the fundamental way to enhance single-sensor performance, which is typically achieved by utilizing a thermal control protocol with a complicated and highly costly apparatus if a millikelvin-level stabilization is required. Here, we analyze the real-time thermal drift and utilize an active way to alternately track the single-spin ESR frequency drift in the experiment. Using this method, we achieve a temperature stabilization effect equivalent to sub-millikelvin (0.8 mK) level with no extra environmental thermal control, and the spin-state readout contrast is significantly improved in long-lasting experiments. This method holds broad applicability for NV-based single-spin experiments and harbors the potential for prospective expansion into diverse nanoscale quantum sensing domains.

Massless spin 2 field in 50-component approach: exact solutions with cylindrical symmetry, eliminating the guage degrees of freedom

We begin with some known results of the 50-component theory for a spin-2 field described in cylindrical coordinates. This theory is based on the use of a 2nd-rank symmetric tensor and a 3rd-rank tensor symmetric in two indices. In the massive case, this theory describes a spin-2 particle with an anomalous magnetic moment. According to the Fedorov – Gronskiy method, which is based on projective operators, all 50 functions involved in the description of the spin-2 field for the case of the free particle can be expressed in terms of only 7 different functions constructed from Bessel functions. This leads to a homogeneous system of linear algebraic equations for 50 numerical parameters. We have found 6 independent solutions to these equations. Additionally, we have obtained explicit expressions for 4 guage solutions defined in accordance with the Pauli – Fierz approach. These solutions are exact and correspond to non-physical states that do not affect observable quantities, such as the energy-momentum tensor. Finally, we have constructed two classes of solutions that represent physically observable states.

Spin–orbit torque effect in silicon-based sputtered Mn3Sn film

Abstract Noncollinear antiferromagnet Mn3Sn has shown remarkable efficiency in charge–spin conversion, a novel magnetic spin Hall effect, and a stable topological antiferromagnetic state, which has resulted in great interest from researchers in the field of spin–orbit torque. Current research has primarily focused on the spin–orbit torque effect of epitaxially grown noncollinear antiferromagnet Mn3Sn films. However, this method is not suitable for large-scale industrial preparation. In this study, amorphous Mn3Sn films and Mn3Sn/Py heterostructures were prepared using magnetron sputtering on silicon substrates. The spin-torque ferromagnetic resonance measurement demonstrated that only the conventional spin–orbit torque effect generated by in-plane polarized spin currents existed in the Mn3Sn/Py heterostructure, with a spin–orbit torque efficiency of 0.016. Additionally, we prepared the perpendicular magnetized Mn3Sn/CoTb heterostructure based on amorphous Mn3Sn film, where the spin–orbit torque driven perpendicular magnetization switching was achieved with a lower critical switching current density (3.9×107 A/cm2) compared to Ta/CoTb heterostructure. This research reveals the spin–orbit torque effect of amorphous Mn3Sn films and establishes a foundation for further advancement in the practical application of Mn3Sn materials in spintronic devices.

Classical Kerr-Schild double copy in bigravity for maximally symmetric spacetimes

A generalized Kerr-Schild ansatz for bigravity, already considered in the literature, which leads to linear interactions between the metrics is used to study the bigravity equations in the context of the double copy. By contracting the resulting spin-2 field bigravity equations of motion using Killing vector fields, as is usually carried out in general relativity, we arrive to the single and zeroth copy equations for the mentioned ansatz. For the case of stationary solutions, we obtain two Maxwell and two conformally coupled scalar field equations for the single and zeroth copies respectively, and the linear interactions are absent. In the time-dependent case we obtain equations for the fields which are coupled. By decoupling these equations and at the zeroth copy level, we recover a massless and a massive field whose mass is proportional to the Fierz-Pauli mass and depends on the coefficients of the interaction potential between the metrics. This has been also previously documented in the literature and is now reinterpreted within the context of the double copy proposal.

Massive carrollian fields at timelike infinity

Motivated by flat space holography, we demonstrate that massive spin-s fields in Minkowski space near timelike infinity are massive carrollian fields on the carrollian counterpart of anti-de Sitter space called Ti. Its isometries form the Poincaré group, and we construct the carrollian spin-s fields using the method of induced representations. We provide a dictionary between massive carrollian fields on Ti and massive fields in Minkowski space, as well as to fields in the conformal primary basis used in celestial holography. We show that the symmetries of the carrollian structure naturally account for the BMS charges underlying the soft graviton theorem. Finally, we initiate a discussion of the correspondence between massive scattering amplitudes and carrollian correlation functions on Ti, and introduce physical definitions of detector operators using a suitable notion of conserved carrollian energy-momentum tensor.

Spin–momentum properties in the gradient-index fiber

The vector characteristics of the kinetic momentum, spin angular momentum (SAM), and light field of a radially polarized vortex beam (RPVB) in the radial gradient-index (GRIN) fiber are analyzed using a unified methodology based on the generalized Huygens-Fresnel principle and the spin-momentum relationship. The kinetic momentum, SAM, transverse-type spin (t-SAM), longitudinal-type spin (l-SAM) and light field contain parallel and perpendicular components to the optical axis in the GRIN fiber. Moreover, the optical spin skyrmion from the SAM, t-SAM, and l-SAM can be observed at the semi-focal plane and the focal plane of the GRIN fiber. To the best of our knowledge, this is the first confirmation of spin skyrmions in the GRIN fiber. The analysis of spin-momentum properties of an RPVB in the GRIN fiber combined with the generalized Huygens-Fresnel principle and the spin-momentum relationship can be applied in describing the vector properties of transmission in atmospheric and optical systems.