Rarita-Schwinger Field Research Articles

On energy and particle production in cosmology: the particular case of the gravitino

It is well-known that the number of particles produced in cosmology, commonly defined in the literature from the Fock space of the instantaneous hamiltonian of the canonically normalized fields, is ambiguous. On the other hand, the energy computed from the energy-momentum tensor should be physical. We compare the corresponding Fock spaces and relate them through a Bogolyubov transformation. We find that for particles of spin 0, 1 and 3/2 the two Fock spaces are different, whereas they are the same for spin 1/2 fermions. For spin 0 and 1, for particles of high momenta the two Fock spaces align, as intuitively expected. For the spin 3/2, one finds two puzzles. The first one is that the two corresponding Fock spaces do not match even in the limit of high momenta. The second is that whereas we provide evidence for the equivalence theorem between longitudinal gravitinos and the goldstino in terms of an exact matching between the lagrangians and the instantaneous hamiltonians for the canonically normalized fields, the energy operator computed from the Rarita-Schwinger action does not seem to be captured in a simple way by the goldstino action. Our results suggest a re-analysis of non-thermal gravitino production in cosmology.

Massless Rarita-Schwinger equations: Half and three halves spin solution

Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -free of arbitrary functions of time- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-1/2 mode via the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.

Quantum tunneling of spin-1/2 and spin-3/2 particles in the black holes of asymptotically safe gravity

Hawking initiated study of radiations from black holes. The black hole thermodynamics holds a significant importance in understanding of quantum nature of gravity. In this article, Hawking radiations have been studied by employing the semi-classical perspective of quantum tunneling. Dirac and Rarita-Schwinger equations have been employed to determine the tunneling probabilities of spin-1/2 and spin-3/2 particles, respectively, in the background of black holes developed in the asymptotically safe gravity. Hawking temperature determined in both cases is in agreement.

Rarita-Schwinger fields on nearly Kähler manifolds

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of Rarita-Schwinger fields coincides with the space of harmonic 3-forms. Applying the same technique to deformation theory, we also find that the space of infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of Killing spinors.

Rarita-Schwinger fields on nearly parallel G2-manifolds

We study Rarita-Schwinger fields on compact nearly parallel G2-manifolds. In order to investigate them, there is need to clarify the relationship between some differential operators for the canonical G2-connection and the Levi-Civita connection. As a result, we identify the space of Rarita-Schwinger fields with a subspace of the eigenspace of the Laplacian. Applying the same technique to the deformation theory that we use to study Rarita-Schwinger fields, we also identify the space of infinitesimal deformations of the Killing spinor. Since there is a one-to-one correspondence between nearly parallel G2-structures and Killing spinors on 7-dimensional spin manifolds, our results imply that infinitesimal deformations of nearly parallel G2-structures are examined in terms of Killing spinors.

Fermionic greybody factors and quasinormal modes of black holes in Kalb–Ramond gravity

In non-minimally coupled Kalb–Ramond (KR) fields, the vacuum expectation value (VEV) leads to spontaneous local Lorentz symmetry violation, resulting in static spherically symmetric solution. In this solution, fermionic greybody factors (GFs) and quasinormal modes (QNMs) are investigated. First, we study the wave dynamics of fermions using the Dirac and Rarita–Schwinger equations. We have derived the equations of effective potential for fermions with different spins. The fermionic GFs radiated by the black holes (BHs) are calculated using rigorous bounds as well as semi-analytic methods. The fermionic QNM of spin- 1/2 of the BHs in the KR gravity was analyzed using the sixth order WKB method. Furthermore, we discuss how Lorentz violating (LV) parameters impact GFs and QNMs. According to our results, the effective potential curve increases significantly when the LV parameter value γ is high. Thus, as the LV parameter γ increases, the bound of the GF and the QNM’s wave oscillation frequency will increase, while the decay rate will slow down.

Sources of torsion in Poincarè gauge gravity

We study sources for torsion in Poincarè gauge theory in any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang–Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita–Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n ge 2k+1 dimensions. For k>0 there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante–Rosenfield energy tensors in terms of different choices of independent variables.

Anomaly inflow of Rarita–Schwinger field in 3 dimensions

Anomaly inflow of Rarita–Schwinger field in 3 dimensions

Hawking radiation of rotating BTZ black hole based on modified dispersion relation and Rarita–Schwinger equation

In this paper, tunneling of fermions from rotating BTZ black hole is investigated using modified dispersion relation (MDR) and Rarita–Schwinger equation. The effect of MDR on the tunneling of fermions raises the Hawking temperature of rotating BTZ black hole. It is observed that the modified Hawking temperature of the black hole depends not only on the radial parameters of the black hole but also on the angular parameters of the black hole and the coupling constant [Formula: see text]. Further, the entropy and the heat capacity of the black hole are also studied.

Greybody factors emitted by a regular black hole in a non-minimally coupled Einstein–Yang–Mills theory

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein–Yang–Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita–Schwinger, as well as Klein–Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schrödinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita–Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schrödinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein–Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential’s shape, which is determined by the parameterization of the model. This is in line with quantum theory.

Fermionic Greybody Factors in Schwarzschild Acoustic Black Holes

In Schwarzschild acoustic black hole (SABH) spacetime, we investigate the wave dynamics for the fermions. To this end, we first take into account the Dirac equation in the SABH by employing a null tetrad in the Newman–Penrose (NP) formalism. Then, we consider the Dirac and Rarita–Schwinger equations, respectively. The field equations are reduced to sets of radial and angular equations. By using the analytical solution of the angular equation set, we decouple the radial wave equations and obtain the one-dimensional Schrödinger-like wave equations with their effective potentials. The obtained effective potentials are graphically depicted and analyzed. Finally, we investigate the fermionic greybody factors (GFs) radiated by the SABH spacetime. A thorough investigation is conducted into how the acoustic tuning parameter affects the GFs of the SABH spacetime. Both the semi-analytic WKB method and bounds for the GFs are used to produce the results, which are shown graphically and discussed.

Scattering of complex gravitino test fields from a gravitational pulse

Gravitational pulse waves are defined as step functions at the boundaries. In this setting, linearized Rarita–Schwinger equations are precisely solved in Rosen coordinates. It is found that the gravitino’s energy–momentum varies with the sandwich wave’s shape. The gravitino’s energy density will decrease as it crosses the sandwich wave at the test field level since the background won’t change.

Generalized Mathisson–Papapetrou–Tulczyjew–Dixon equations

We derive two generalizations of Mathisson–Papapetrou–Tulczyjew–Dixon equations from Casalbuoni–Brink–Schwarz type pseudoclassical Lagrangians of Majorana spinors on a Riemann–Cartan spacetime. One has an additional gauge freedom, which makes the equations of motion also be a generalization of Wong’s equations. The other is a spinor model coupled with a Rarita–Schwinger field to preserve the supersymmetry. The coupling to the torsion is modified due to the existence of the Rarita–Schwinger field. In both extensions, the Tulczyjew condition is automatically satisfied.

An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon

The phenomenon of gravitational particle production can take place for quantum fields in curved spacetime. The abundance and energy spectrum of gravitationally produced particles is typically calculated by solving the field’s mode equations on a time-dependent background metric. For purposes of studying dark matter production in an inflationary cosmology, these mode equations are often solved numerically, which is computationally intensive, especially for the rapidly-oscillating high-momentum modes. However, these same modes are amenable to analytic evaluation via the Exact Wentzel-Kramers-Brillouin (EWKB) method, where gravitational particle production is a manifestation of the Stokes phenomenon. These analytic techniques have been used in the past to study gravitational particle production for spin-0 bosons. We extend the earlier work to study gravitational production of spin-1/2 and spin-3/2 fermions. We derive an analytic expression for the connection matrix (valid to all orders in an adiabatic parameter ħ) that relates Bogoliubov coefficients across a Stokes line connecting a merged pair of simple turning points. By comparing the analytic approximation with a direct numerical integration of the mode equations, we demonstrate an excellent agreement and highlight the utility of the Stokes phenomenon formalism applied to fermions. We discuss the implications for an analytic understanding of catastrophic particle production due to vanishing sound speed, which can occur for a spin-3/2 Rarita-Schwinger field.

On commutator-based linearization of vector-spinor nonlinear supersymmetry and Rarita–Schwinger fields

In this paper, we discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both [Formula: see text] and [Formula: see text]-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu–Goldstone (NG) fermions, which are expressed as simple products of powers of the spin-3/2 NG fermions and a fundamental determinant in the vsNLSUSY theory. We define basic component fields by means of those functionals in a linearized vsSUSY theory including spin-3/2 fields, general auxiliary ones and a [Formula: see text]-term. The general forms of linear (rigid) vsSUSY transformations for the component fields are determined uniquely from the commutator-based linearization procedure. By considering appropriate recombinations of the functionals of the spin-3/2 NG fermions for [Formula: see text] SUSY, we find that variations of the recombinations under the vsNLSUSY transformations include linear spin-1/2 SUSY ones of spin-[Formula: see text] fields with [Formula: see text] gauge invariance. The spinorial gauge invariance of the Rarita–Schwinger action in the linearization process is also discussed together with the [Formula: see text] gauge invariance.

Magnetic charges in supergravity

In this paper we study the dual charges of mathcal{N} = 1 supergravity in asymptotically flat space-time. The action considered is the usual supergravity action with a topological contribution. This is the Nieh-Yan term and the magnetic term of the free Rarita-Schwinger field. Through methods of the covariant phase space formalism we construct the charges conjugate to supersymmetry, diffeomorphism and Lorentz transformations. The additional term in the action will lead to new, non-vanishing contributions to these charges. The magnetic diffeomorphism charges are equivalent to the ones previously found for gravity, while the dual supersymmetric charges are new and do not appear for the free Rarita-Schwinger field. The dual Lorentz charges serve to regularize the previous two. We find that the asymptotic symmetry group for supergravity can only include globally well-defined super-rotations.

Analytic formula for quasinormal modes in the near-extreme Kerr-Newman–de Sitter spacetime governed by a non-Pöschl-Teller potential

Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the P\"oschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the P\"oschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is valid for both bosonic and fermionic fields. We further extend the analysis to the case of charged rotating black holes and find a general analytical formula for quasinormal modes of the fields of various spin for the near extreme Kerr-Newman-de Sitter spacetime.

Chiral vortical effect in extended Rarita-Schwinger field theory and chiral anomaly

We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $\mu^2$ and $T^2$ are proportional to each other, but not proportional to the spin, which indicates a possible new universality between the temperature-related and the chemical potential-related vortical effects. The results obtained allow us to speculate about the relationship between the gauge and gravitational chiral anomalies.

Asymptotic symmetries at null-infinity for the Rarita–Schwinger field with magnetic term

In this paper we study the magnetic charges of the free massless Rarita–Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang–Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

Unification of massless field equations solutions for any spin

A unification in terms of exact solutions for massless Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre-potential functions, which satisfy the d'Alembert equation. The coupled equations satisfied by the pre-potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre-potentials that satisfy the usual wave equation which may be used to construct exact non-trivial solutions to Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to a unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre-potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.