Spinor Fields Research Articles

Generalized Siklos space-times

Abstract Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex function. We call the resulting geometry a generalized Siklos space-time. After deriving a number of identities for complex spaces, we specialize to Lorentz signature, where we show that the Killing function must be real and that the corresponding Dirac spinor is Majorana (as long as the space-time is not conformally flat), and we obtain the local form of the metric. We show that the purely gravitational degrees of freedom correspond to waves, whereas the matter sources generically correspond, via Einstein’s field equations, to a sum of pure radiation and a space-like perfect fluid. Consequently, we conclude that the physically relevant case is obtained when the Killing function is homogeneous on the wave surfaces.

Introduction to Thermal Field Theory: From First Principles to Applications

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory.

Dual Lagrangian formulations for free massive fields of higher spins in three dimensions

Dual Lagrangian formulations for free massive fields of higher spins in three dimensions

Catalog-based pseudo-Cℓ s

We present a formalism to extract the angular power spectrum of fields sampled at a finite number of points with arbitrary positions — a common situation for several catalog-based astrophysical probes — through a simple extension of the standard pseudo-Cℓ algorithm. A key complication in this case is the need to handle the shot noise component of the associated discrete angular mask which, for sparse catalogs, can lead to strong coupling between very different angular scales. We show that this problem can be solved easily by estimating this contribution analytically and subtracting it. The resulting estimator is immune to small-scale pixelization effects and aliasing, and, most notably, unbiased against the contribution from measurement noise uncorrelated between different sources. We demonstrate the validity of the method in the context of cosmic shear datasets, and showcase its usage in the case of other spin-0 and spin-1 astrophysical fields of interest. We incorporate the method in the public <monospace>NaMaster</monospace> code.

Spinning up the spool: massive spinning fields in 3d quantum gravity

Spinning up the spool: massive spinning fields in 3d quantum gravity

Exotic supergravities and the Swampland

In six dimensions, there is an exotic N = (4, 0) supermultiplet that contains only fields of spin ≤ 2, but no graviton, and that on a circle reduces to 5D N = 4 supergravity. It has been proposed that, if suitable interactions exist, the (4, 0) theory might provide a consistent alternative UV completion for N = 4 5D supergravity, realizing a supersymmetric version of asymptotic safety. In this note we argue that any Lorentz-invariant (4, 0) theory (interacting or not) carries an exact global symmetry when compactified on S1, and is therefore incompatible with the Swampland no global symmetries conjecture. Another example of exotic supergravity, the 6D (3, 1) theory, evades our simple criterion. We study the general case and find that the only exotic spin-2 field that reduces to Einsteinian gravity and, in the absence of supersymmetry, potentially has no global symmetries when compactified on a high-dimensional torus is that which appears in the (3, 1) multiplet. All other possibilities either yield several gravitons or have global symmetries.

Thermal one-point functions and their partial wave decomposition

In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on S1 × Sd−1. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposition of one-point functions of the scalar ϕ2 and the stress tensor T for a three-dimensional free scalar field ϕ. We are able to read off averaged OPE coefficients into exchanged fields of high weight and spin for a complete set of tensor structures. We also extract an asymptotic behaviour of conformal blocks and use it to analyse the density of heavy-heavy-light OPE coefficients for spinning operators, comparing it with semi-classical predictions, such as the dimensions of operators at large charge.

Pseudo-Conformal Field Theory

Abstract Starting from the observation that the 2-d Polyakov action is metric independent without being topological, while the 4-d Weyl-conformal action is not metric independent, I searched for a 4-d structure and field equation which would be metric independent. I found that the structure is the existence of a geodetic and shear-free Newman-Penrose (NP) null tetrad, which is a Frobenius integrable structure, called lorentzian Cauchy-Riemann (LCR) structure. The metric independent equation is a gauge field equation identified with the gluon field. Imposing the LCR-structure as the fundamental structure of nature (instead of the Einstein-metric) all the interactions (gravity, electroweak and gluonic) are derived. The three generations of the leptons are solitonic configurations with precise topological invariants. The quarks are confined sources of the gluonic field implied by the LCR-tetrad of the corresponding leptons. Quantum field theory emerges through the Bogoliubov causal approach and the standard model is derived through the Scharf procedure of the Kugo-Ojima BRS elimination technique of the unphysical modes of the spin-1 and spin-2 fields.

Modeling the 3-point correlation function of projected scalar fields on the sphere

One of the main obstacles for the signal extraction of the three point correlation function using photometric surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST), will be the prohibitive computation time required for dealing with a vast quantity of sources. Brute force algorithms, which naively scales as 𝒪(N 3) with the number of objects, can be further improved with tree methods but not enough to deal with large scale correlations of Rubin's data. However, a harmonic basis decomposition of these higher order statistics reduces the time dramatically, to scale as a two-point correlation function with the number of objects, so that the signal can be extracted in a reasonable amount of time. In this work, we aim to develop the framework to use these expansions within the Limber approximation for scalar (or spin-0) fields, such as galaxy counts, weak lensing convergence or aperture masses. We develop an estimator to extract the signal from catalogs and different phenomenological and theoretical models for its description. The latter includes halo model and standard perturbation theory, to which we add a simple effective field theory prescription based on the short range of non-locality of cosmic fields, significantly improving the agreement with simulated data. In parallel to the modeling of the signal, we develop a code that can efficiently calculate three points correlations of more than 200 million data points (a full sky simulation with Nside=4096) in ∼40 minutes, or even less than 10 minutes using an approximation in the searching algorithm, on a single high-performance computing node, enabling a feasible analysis for the upcoming LSST data.

On the realization of infinite (continuous) spin field representations in AdS space

On the realization of infinite (continuous) spin field representations in AdS space

Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces

We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-0 fields (solutions to the wave equation) on n-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions written in terms of series expansions close to spatial and null infinity and use them to compute non-trivial asymptotic spin-0 charges. It is shown that if one examines the most general initial data within the class considered in this paper, the expansion is polyhomogeneous and hence of restricted regularity at null infinity. Furthermore, we derive the conditions on the initial data needed to obtain well-defined limits for the asymptotic charges at the critical sets where null infinity and spatial infinity meet. In four dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for higher dimensions there is only a finite number of non-trivial asymptotic charges with well-defined limits at the critical sets.

Symmetric vs. chiral approaches to massive fields with spin

Abstract Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance.

Exploring a novel Einstein–Rosen BTZ wormhole

We introduce a novel Einstein–Rosen BTZ wormhole metric as a solution to the Einstein field equations with a negative cosmological constant and explore in detail its various phenomenological aspects. We show that the wormhole metric is characterized by a horizon at the throat, resembling a black hole horizon. This implies that our wormhole metric describes a one-way traversable wormhole at the throat, with Hawking radiation observed by an observer located at some distance from the wormhole. It is also found the same Hawking temperature using the BTZ-like coordinates and Kruskal-like coordinates. This temperature is invariant not only on the type of coordinates but also the nature of the spin of quantum fields. Importantly, we find that at the wormhole throat, the spacetime is not a pure vacuum solution, but rather contains an exotic string matter source with negative tension, which may stabilize the wormhole geometry. To this end, we found that the size of the wormhole throat is proportional to the number of quantum bits suggesting a possible implications on ER=EPR. Further we studied the particle dynamics and, finally, we tested the ANEC with a test scalar and vector fields. For the double null-component computed in BTZ coordinates, we found an apparent divergence at the wormhole throat, which is then shown to be regularized by means of Kruskal-like coordinates. The ANEC for such a scalar/vector field is violated at the wormhole throat.

Crystal field and microscopic spin Hamiltonians approach for V3+ ions in α-ZnAl2S4 single crystals

The optical properties of α-ZnAl2S4:V3+ single crystals were investigated by S. Angel et al. (Anghel et al., 2011) [1]. The spectra of α-ZnAl2S4:V3+ reveal electronic transitions between the energy levels of V3+ ions located at the octahedral site. A comprehensive theoretical study was performed, examining crystal field, spin-spin and other spin orbit interactions. The calculated energy level schemes significantly correspond with the experimental results of V3+ doped α-ZnAl2S4 at both low and room temperatures. A novel, consistent interpretation of the radiative properties is proposed, considering the effect of temperature on crystal field parameters. This interpretation supports the potential use of α-ZnAl2S4: V3+ single crystals, excited at λex = 532 nm, as active media in tunable lasers and amplifiers.

Classical characters of spinor fields in torsion gravity

Abstract We consider the problem of having relativistic quantum mechanics re-formulated with hydrodynamic variables, and specifically the problem of deriving the Mathisson–Papapetrou–Dixon equations (describing the motion of a massive spinning body moving in a gravitational field) from the Dirac equation. The problem will be answered on a general manifold with torsion and gravity. We will demonstrate that when plane waves are considered the MPD equations describe the general relativistic wave-particle duality with torsion (Guedes and Popławski 2024 Class. Quantum Grav. 41 065011), but we will also see that in such a form the MPD equations become trivial.

Cubic interactions for massless and partially massless spin-1 and spin-2 fields

We perform a complete classification of the consistent two-derivative cubic couplings for a system containing an arbitrary number of massless spin-1, massless spin-2, and partially massless (PM) spin-2 fields in D-dimensional (anti-)de Sitter space. In addition to previously known results, we find a unique candidate mixing between spin-1 and PM spin-2 fields. We derive all the quadratic constraints on the structure constants of the theory, allowing for relative “wrong-sign” kinetic terms for any of the fields. In the particular case when the kinetic terms in each sector have no relative signs, we find that the unique consistent non-trivial theory is given by multiple independent copies of conformal gravity coupled to a Yang-Mills sector in D = 4. Our results strengthen the well-known no-go theorems on the absence of mutual interactions for massless and PM spin-2 fields.

Unveiling the Effects of Coupling Extended Proca-Nuevo Gravity on Cosmic Expansion with Recent Observations

Abstract We study Coupling Extended Proca-Nuevo gravity, a non-linear theory extending from dRGT massive gravity with a spin-1 field. This theory is shown to yield reliable, ghost-free cosmological solutions, modeling both the Universe’s thermal history and late-time acceleration. By analyzing data from Dark energy spectroscopic instruments (DESI), Cosmic Chronometer (CCh), Gamma Ray Bursts (GRBs), and Type Ia Supernova (SNeIa), we derive parameter constraints with up to 3σ confidence, demonstrating good agreement with observations. Our comparison of BAO data from WiggleZ and DESI highlights its constraining power on the Hubble constant. The analysis of the cosmographic parameter, q shows the statistical compatibility with the recent data. Further, this indicates that Universe’s current accelerated expansion aligns with quintessential behavior.

Periodic skyrmionic textures via conformal cartographic projections

We find periodic skyrmionic textures via conformal cartographic projections that map either an entire spherical parameter space or a hemisphere onto every regular polygon that provides regular tessellations of the plane. These textures minimize the energy inherent to the mapping and preserve the sign of the Skyrme density throughout the entire space. We show that 2D spinor fields (e.g., 2D polarization) that present periodic textures preserving the sign of the Skyrme density unavoidably exhibit zeros. We implement these textures in the polarization state of a laser beam.

Application of Reservoir Computers for Chaos Synchronization and Cracking Chaos-Based Cryptography in Fermionic 2D Thirring and 4D Gursey Models with Spinor Fields

Reservoir computers have recently become one of the most widely exploited model-free approaches to chaos synchronization due to their fast convergence speed and simple yet effective learning rules. In this study, reservoir computing has been utilized to emulate the dynamics of chaotic Thirring and Gursey systems. In the supervised learning of the reservoir, one-step ahead states of the dynamical systems have been employed as the teaching signals. After the training phase, the reservoir was first run autonomously and then weakly driven by chaotic systems. It has been shown that the trained reservoir computers can exhibit the same characteristics as the attractors of the learned chaotic systems, which enable their use in synchronization tasks of chaotic systems with possible application in cracking chaos-based cryptography. To investigate the effect of noise on the performance of reservoir computers, noise signals with different colors and amplitudes have been included in the transmitted signals. The obtained results indicate that the proposed scheme can provide lower error metrics for both models.

Klein–Gordon equation in the presence of a vector generalized Yukawa and a scalar generalized Hulthen potentials in the rotating cosmic string space–time

In this paper, we explore the relativistic quantum dynamics of spin-0 oscillator fields within the framework of a rotating cosmic string space–time, taking into account the presence of scalar and vector potentials. We solve the Klein–Gordon oscillator equation in this curved space–time, incorporating generalized versions of the Yukawa and Hulthen potentials as vector and scalar potentials, respectively. The analytical solution of the quantum system yields the energy eigenvalue and corresponding eigenfunction, which is expressed in terms of confluent Heun functions. The resulting energy spectrum is shown to depend on various parameters associated with the cosmic string space–time and the confining potentials. We graphically illustrate how the energy spectrum varies with changes in both the potential parameters and the cosmic string parameters.