Rarita Schwinger Research Articles

Spinor description of the curvatures of D = 5 gauge fields

Spinor description of the curvatures of D = 5 Yang–Mills, Rarita–Schwinger and gravitational fields is considered. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are studied. In the absence of sources symmetric curvature spinors with 2s indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to 4d case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold SO(1, 4)/(SO(1,1) × ISO(3)) isomorphic to the three-sphere is considered.

Counterpart of the Weyl tensor for Rarita–Schwinger type fields

In dimensions larger than 3 a modified field strength for Rarita–Schwinger type fields is constructed whose components are not constrained by the field equations. In supergravity theories the result provides a modified (supercovariant) gravitino field strength related by supersymmetry to the (supercovariantized) Weyl tensor. In various cases, such as for free Rarita–Schwinger type gauge fields and for gravitino fields in several supergravity theories, the modified field strength coincides on-shell with the usual field strength. A corresponding result for first order derivatives of Dirac type spinor fields is also presented.

Inconsistency of the ‘spin-3/2 gauge invariant’ interaction of Rarita–Schwinger fields

We perform the Dirac quantization of Rarita–Schwinger fields interacting with a spinor and the first derivative of a pseudoscalar field. We achieve the calculations for two forms of this interaction: first we review the conventional coupling of lowest derivative order, reproducing the well known inconsistencies in its anticommutator algebra. Then, we perform the analysis on the next order term popularly known as ‘spin-3/2 gauge invariant interaction’, which is claimed to be free of these inconsistencies. Nevertheless we find that the direct application of the Dirac formalism leads to inconsistencies in complete analogy to the previous case. This is of high relevance in the particle phenomenology field, where these interactions are used to interpret experimental data involving resonances.

Relativistic wave equations of arbitrary spin in quantum mechanics and field theory, example spin s=2

Relativistic wave equations for the particles of arbitrary spin suggested by Bhabha, Bargmann–Wigner, Rarita–Schwinger (for spin s = 3/2) and other authors are under consideration. The comparison with the equations introduced recently by the author in Ukr. J. Phys., Vol. 60, N 10. 985–1006 (2015) and J. Phys.; Conf. Ser. Vol. 670, 012047(1–16) (2016) is given. The advantages of the new equations are considered brie y. The three level consideration (relativistic canonical quantum mechanics, canonical Foldy–Wouthuysen type field theory, locally covariant field theory) is presented. The operator link between the relativistic canonical quantum mechanics and locally covariant field theory of arbitrary spin is found. This link is given by the extended Foldy–Wouthuysen transwormation between the 2(2s+1)- component local field theory and the corresponding relativistic canonical quantum mechanics. The important partial example of spin s=2 case is considered in details. The 10-component Dirac-like wave equation for the spin s=(2,2) particle-antiparticle doublet is suggested. The link with 10-component Maxwell-like equation for this doublet is considered brifly. The hypothesis on the spin s=5/2 particle is discussed.

The generalized uncertainty relation and the quantum entropy of static spherical black hole surrounded by quintessence due to spin fields

By using the brick-wall model, the quantum entropies of static spherical black hole surrounded by quintessence due to the Weyl neutrino, electromagnetic, massless Rarita–Schwinger, and gravitational fields for the source-free case are investigated from a generalized uncertainty relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic, and logarithmic divergences at ultraviolet σ → 0, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. After the smallest length scale is taken into account, we find that the contribution of the gravitational interactions to the entropy is larger than the usual dominant term and becomes a part of the whole dominant term, so it is very important and cannot be neglected.

Faddeev–Jackiw Hamiltonian reduction for free and gauged Rarita–Schwinger theories

We study the Faddeev-Jackiw symplectic Hamiltonian reduction for 3+1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structure of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita-Schwinger theory cannot be obtained in a covariant way.

Spinor description of D = 5 massless low-spin gauge fields

Spinor description for the curvatures of D = 5 Yang–Mills, Rarita–Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere is proposed. The states in its spectrum are given by the functions on S3 that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various supermultiplets of D = 5 space–time supersymmetry.

Rarita–Schwinger massless field in covariant and Coulomb-like gauges

The massless Rarita–Schwinger field propagator used in perturbative interacting field theories involving this field is derived in covariant and the Coulomb-like gauges for the first time by explicitly invoking the gauge constraints as it was for a massless vector field over the years.

Spontaneous excitation of a detector in circular motion coupled to massless Rarita–Schwinger fields in vacuum

We study the spontaneous excitation of a detector (modeled by a two-level atom) in circular motion coupled nonlinearly to vacuum massless Rarita–Schwinger fields in the ultrarelativistic limit and demonstrate that the spontaneous excitation occurs for ground-state atoms in circular motion in vacuum but the excitation rate is not of a pure thermal form as that of the atoms in linear uniform acceleration. An interesting feature is that terms of odd powers in acceleration appear in the excitation rate whereas in the linear acceleration case there are only terms of even powers present. On the other hand, what makes the present case unique in comparison to the atom’s coupling to other fields that are previously studied is the appearance of the terms proportional to the seventh and ninth powers of acceleration in the mean rate of change of atomic energy which are absent in the scalar, electromagnetic and Dirac field cases.

Consistency of matter models with asymptotically safe quantum gravity

We discuss the compatibility of quantum gravity with dynamical matter degrees of freedom. Specifically, we present bounds we obtained in Donà et al. (Phys. Rev. D, 89, 084035 (2014) doi:10.1103/PhysRevD.89.084035 ) on the allowed number and type of matter fields within asymptotically safe quantum gravity. As a novel result, we show bounds on the allowed number of spin-3/2 (Rarita–Schwinger) fields (e.g., the gravitino). These bounds, obtained within truncated renormalization group flows, indicate the compatibility of asymptotic safety with the matter fields of the standard model. Further, they suggest that extensions of the matter content of the standard model are severely restricted in asymptotic safety. This means that searches for new particles at colliders could provide experimental tests for this particular approach to quantum gravity.

Propagation peculiarities of mean field massive gravity

Massive gravity (mGR) describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR) propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR) which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.

Accelerating black holes, spin-$\frac32$ fields and C-metric

We consider spin-[Formula: see text] particles on the background of general accelerating black holes and the C-metric. The Rarita–Schwinger equations of spin-[Formula: see text] particles are analyzed on these backgrounds. The emission and absorption probabilities of these particles on these spacetimes are calculated. These backgrounds which we analyze contain both black hole horizon and acceleration horizon, and have general electric and magnetic charges, rotation, and acceleration parameter. Other physical quantities of the spin-[Formula: see text] field near the acceleration horizon are also computed.

Generalised Maxwell Equations in Higher Dimensions

This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension $$m$$ and their connections with the Rarita–Schwinger equation. This is done using the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the spin group can be realised in terms of polynomials satisfying a system of differential equations. This allows the construction of generalised wave equations in terms of the unique conformally invariant second-order operator acting on harmonic-valued functions. We prove the ellipticity of this operator and use this to investigate the kernel, focusing on both polynomial solutions and the fundamental solution.

Response of a uniformly accelerated detector to massless Rarita–Schwinger fields in vacuum

We study the response of a uniformly accelerated detector modeled by a two-level atom nonlinearly coupled to vacuum massless Rarita–Schwinger fields. We first generalize the formalism developed by Dalibard, Dupont-Roc, and Cohen-Tannoudji in the linear coupling case, and we then calculate the mean rate of change of the atomic energy of the accelerated atom. Our result shows that a uniformly accelerated atom in its ground state interacting with vacuum Rarita–Schwinger field fluctuations would spontaneously transition to an excited state and the unique feature in contrast to the case of the atom coupled to the scalar, electromagnetic and Dirac fields is the appearance of terms in the excitation rate which are proportional to the sixth and eighth powers of acceleration.

FERMIONS VIA SPINOR-VALUED ONE-FORMS

Spinor-valued one-forms (Rarita–Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a field contains both a spin 1/2 and a spin 3/2 component, and the Rarita–Schwinger Lagrangian is designed to make only the spin 3/2 propagate. The opposite construction is also known to be possible. We propose and study a new simple spinor-valued one-form field Lagrangian that describes a propagating spin 1/2 particle.

Some Rarita–Schwinger Type Operators

In this paper we study a generalization of the classical Rarita–Schwinger type operators and construct their fundamental solutions. We give some basic integral formulas related to these operators. We also establish that the projection operators appearing in the Rarita–Schwinger operators and the Rarita–Schwinger equations are conformally invariant. We further obtain the intertwining operators for other operators related to the Rarita–Schwinger operators under actions of the conformal group.

On the fundamental solution for higher spin Dirac operators

In this paper, we will determine the fundamental solution for the higher spin Dirac operator Qλ, which is a generalisation of the classical Rarita–Schwinger operator to more complicated irreducible (half-integer) representations for the spin group in m dimensions. This will allow us to generalise the Stokes theorem, the Cauchy–Pompeiu theorem and the Cauchy integral formula, which lie at the very heart of the function theory behind arbitrary elliptic higher spin operators.

Rarita–Schwinger particles under the influence of strong magnetic fields

In this work, we calculate the solutions of the Rarita–Schwinger equation with the inclusion of the electromagnetic interaction. Our gauge and coupling prescription choices lead to Dirac-type solutions. One of the consequences of our results is that all inconsistencies related to noncovariance and noncausality are avoided, and the Landau level occupation of particles turns out to be quite different from the usual spin 1/2 particle system occupation numbers. Our results do not indicate that the well known results obtained by Velo and Zwanzinger in 1969 are false or incorrect; they rather indicate that there exists an alternative way to deal with this problem that should be further explored, since this is a matter of interest in recent results related to heavy ion collisions and nuclear astrophysics.

Towards loop quantum supergravity (LQSG): II. p-form sector

In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantization of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantization of the 3-index photon of minimal 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern–Simons term for the 3-index photon, which is due to local SUSY, the theory is self-interacting and its quantization far from straightforward. Nevertheless, we show that a reduced phase space quantization with respect to the 3-index photon Gauß constraint is possible. Specifically, the Weyl algebra of observables, which deviates from the usual CCR Weyl algebras by an interesting twist contribution proportional to the level of the Chern–Simons theory, admits a background independent state of the Narnhofer–Thirring type.

Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector

In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11 D SUGRA and 4 D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita–Schwinger field. This is non-trivial because SUSY typically requires the Rarita–Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.