Massless Rarita-Schwinger Research Articles

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.

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.

Chiral separation effect for spin 3/2 fermions

Chiral Separation Effect (CSE) for systems that feature spin 3/2 fermions was considered. For the self-consistent Adler’s model with relativistic massless Rarita-Schwinger fermions (RSA model), we found that the CSE conductivity is five times larger than for massless Dirac fermions. For a model of four-fold band crossing in Rarita-Schwinger-Weyl semimetals, in which massless fermions with quasispin 3/2 exist, we calculated that the CSE conductivity is four times larger than for Weyl fermions. We show that CSE conductivity for any multi-degenerate Fermi point in topological semimetals is proportional to its Chern number and is topologically protected. Along the calculations, we proved an index theorem that relates Chern number of a Fermi-point and spectral asymmetry of the corresponding Landau band structure. The assumption that CSE for any system of chiral fermions is dictated by the corresponding Chern number is found to be correct for RSA model (and for the Dirac fermions).

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

We construct the Rarita–Schwinger basis vectors, [Formula: see text], spanning the direct product space, [Formula: see text], of a massless four-vector, [Formula: see text], with massless Majorana spinors, [Formula: see text], together with the associated field-strength tensor, [Formula: see text]. The [Formula: see text] space is reducible and contains one massless subspace of a pure spin-[Formula: see text]. We show how to single out the latter in a unique way by acting on [Formula: see text] with an earlier derived momentum independent projector, [Formula: see text], properly constructed from one of the Casimir operators of the algebra [Formula: see text] of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless [Formula: see text] carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as [Formula: see text]. The conclusion is that the [Formula: see text] bi-vector spinor field can play the same role with respect to a [Formula: see text] gauge field as the bi-vector, [Formula: see text], associated with the electromagnetic field-strength tensor, [Formula: see text], plays for the Maxwell gauge field, [Formula: see text]. Correspondingly, we find the free electromagnetic field equation, [Formula: see text], is paralleled by the free massless Rarita–Schwinger field equation, [Formula: see text], supplemented by the additional condition, [Formula: see text], a constraint that invokes the Majorana sector.

Spin raising and lowering operators for Rarita-Schwinger fields

Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-$\frac{3}{2}$ massless Rarita-Schwinger equation from source-free Maxwell fields and twistor spinors are constructed. It is shown that this construction requires Ricci-flat backgrounds due to the gauge invariance of the massless Rarita-Schwinger equation. Constraints to construct spin raising and lowering operators for Rarita-Schwinger fields are found. Symmetry operators for Rarita-Schwinger fields via twistor spinors are obtained.

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.

More on non-supersymmetric asymmetric orbifolds with vanishing cosmological constant

We explore various non-supersymmetric type II string vacua constructed based on asymmetric orbifolds of tori with vanishing cosmological constant at the one loop. The string vacua we present are modifications of the models studied in arXiv:1512.05155[hep-th], of which orbifold group is just generated by a single element. We especially focus on two types of modifications: (i) the orbifold twists include different types of chiral reflections not necessarily removing massless Rarita-Schwinger fields in the 4-dimensional space-time, (ii) the orbifold twists do not include the shift operator. We further discuss the unitarity and stability of constructed non-supersymmetric string vacua, with emphasizing the common features of them.

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.

Classical gauged massless Rarita-Schwinger fields

We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields consistent classical and quantum theories, with a generalized fermionic gauge invariance. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. The quantized case is studied in gauge covariant radiation gauge and $\Psi_0=0$ gauge for the Rarita-Schwinger field, by both functional integral and Dirac bracket methods. In $\Psi_0=0$ gauge, the constraints have the form needed to apply the Faddeev-Popov method for deriving a functional integral. The Dirac bracket approach in $\Psi_0=0$ gauge yields consistent Hamilton equations of motion, and in covariant radiation gauge leads to anticommutation relations with the correct positivity properties. We discuss relativistic covariance of the anticommutation relations, and of Rarita-Schwinger scattering from an Abelian potential. We note that fermionic gauge transformations are a canonical transformation, but further details of the transformation between different fermionic gauges are left as an open problem.

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.

Spin field equations and Heun’s equations

The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino (s=1/2), electromagnetic (s=1), Rarita-Schwinger (s=3/2), and gravitational (s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun’s equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.

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.

The generalized uncertainty principle and the quantum entropy due to spin fields on the Reissner-Nordström black hole background

By using the null tetrad and the ’t Hooft brick-wall model, the quantum entropies of a Reissner-Nordstrom black hole due to the Weyl neutrino, electromagnetic, massless Rarita-Schwinger and gravitational fields for the source-free case are investigated from a generalized uncertainty principle. The divergence structure for the entropy is demonstrated. In addition to the usual linearly and logarithmically divergent terms, additional quadratic, cubic, biquadratic and other higher order divergences exist near the event horizon in the entropy, which not only depend on the black hole characteristics but also on the spin fields and the gravitational interactions. The terms describe the contribution of the quantum fields to the entropy and the effects of the generalized uncertainty principle on it. If the smallest length scale is taken into account, the contribution of the gravitational interactions to the entropy is found to be a part of the dominant term and very important, and therefore it can not be neglected.

All the Fundamental Massless Fermion Fields in Superstring Theory: A Rigorous Analysis

A systematic rigorous analysis of both massless fermion fields in the mass spectra of superstring theory is carried out. Our interest is in dynamical aspects of these fields. An explicit novel expression for the propagator of the massless Rarita-Schwinger field (the gravitino), in the mass spectrum involving massless fermions in superstring theory in 10 dimensions, is derived. The analysis is carried in the presence of a non-constrained external source so that the full expression of the propagator emerges. The number of associated degrees of freedom is also obtained. We work in a Coulomb-like gauge. The massless Dirac field (the dilatino), the other massless fermion field in the mass spectra of superstring theory in 10 dimensions, is first investigated to this end.

The generalized uncertainty principle and the thermodynamic quantities near a black hole

The thermodynamic quantities for the Weyl neutrino, electromagnetic, massless Rarita-Schwinger and gravitational fields around a Reissner-Nordstrom-de Sitter black hole are investigated by using the modified state density due to a generalized uncertainty principle. It is shown that in addition to the usual leading term, there exist additional terms in any one of these equations, which give the effects of the spin fields and the generalized uncertainty principle on the thermodynamical quantities. The terms not only depend on the black hole characteristics but also on the spin of the field and the gravity correction factor, and they are important and cannot be neglected. In curved spacetime, the thermodynamic quantities do not take the same form as that in flat spacetime. Moreover, the new equation of state demonstrates that the trace of the stress tensor is non-zero.

Modifications to the Thermodynamic Quantities around Reissner–Nordström Black Holes Due to the Generalized Uncertainty Principle

The thermodynamic quantities for the Weyl neutrino, electromagnetic, massless Rarita–Schwinger and gravitational fields around a Reissner–Nordstrom black hole are investigated by using the modified state density due to a generalized uncertainty principle. In addition to the usual leading term, these quantities include additional modifications, which not only depend on the black hole characteristics but also on the spin of the field and the gravity correction factor. Moreover, the new equation of state showes that the trace of the stress tensor is non-zero. The result is consistent with the conformal anomaly.

ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

Four-dimensional couplings among BF and massless Rarita–Schwinger theories: a BRST cohomological approach

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a free model that describes a massless Rarita-Schwinger theory and an Abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.

No cross-interactions between the Weyl graviton and the massless Rarita-Schwinger field

The proof of the fact that there are no nontrivial, consistent cross-couplings that can be added between the Weyl graviton and the massless Rarita-Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield-Becchi-Rouet-Stora-Tyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincare invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost number zero).