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).
We review the general heat kernel method for the Dirac spinor field as an elementary example in any arbitrary background. We, then compute the first three Seeley-DeWitt coefficients for the massless free spin-3/2 Rarita-Schwinger field without imposing any limitations on the background geometry.
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 s…
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.
We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension $\frac{1}{2}$ auxiliary spin-$\frac{1}{2}$ field $Λ$, in which there is an exact off-shell gauge invariance. In $Λ=0$ gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsing…
We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Gal…
Fermion-fermion scattering in a Rarita-Schwinger model with Yukawa-like interaction
Universidade Federal do Cariri（卡鲁伊里联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Instituto de Física, Universidade Federal de Alagoas（阿拉戈阿斯联邦大学物理研究所）
We recalculate the chiral anomaly in the Abelian gauge model in which a spin-$\frac{1}{2}$ field is directly coupled to a Rarita-Schwinger spin-$\frac{3}{2}$ field, using the extended theory in which there is an exact fermionic gauge invariance. Since the standard gauge fixing and ghost analysis applies to this theory, the ghost contribution to the chiral anomaly is $-1$ times the standard chiral anomaly for spin-$\frac{1}{2}$. Calculation of the fermion loop Feynman diagrams contributing to the coupled model anomaly gives a result of $6$ times the standard anomaly, so the total anomaly is $5$…
We study the Rarita-Schwinger operator on compact Riemannian spin manifolds. In particular, we find examples of compact Einstein manifolds with positive scalar curvature where the Rarita-Schwinger operator has a non-trivial kernel. For positive quaternion Kähler manifolds and symmetric spaces with spin structure we give a complete classification of manifolds admitting Rarita-Schwinger fields. In the case of Calabi-Yau, hyperkähler, $G_2$ and Spin(7) manifolds we find an identification of the kernel of the Rarita-Schwinger operator with certain spaces of harmonic forms. We also give a classific…
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.
We consider the sets of Dirac-Maxwell and Rarita-Schwinger-Maxwell equations in $\mathbb{R} \times S^3$ spacetime. Using the Hopf coordinates, we show that these equations allow separation of variables and obtain the corresponding analytic and numerical solutions. It is also demonstrated that the current of the Dirac field is related to the Hopf invariant on the $S^3 \rightarrow S^2$ fibration.
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-Schwing…
We discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both $N = 1$ and $N$-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 $D$-term. The general forms of linear (rigid) …
We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using the Freudenthal's formula and branching rules. As examples, we calculate the spectra on the sphere, the complex projective space, and the quaternionic projective space.
In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the `pole-skipping' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from …
We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation equivalent to the original equation, and classify first order operators commuting with it in four dimensions. In general such operators are symmetry operators of the original operator, but we find that some of them commute with it. We extend this result in four dimensions to arbitrary dimensions and give first order commuting operators constructed of odd ran…
A critique on the supplementary conditions of Rarita-Schwinger framework
在简要回顾了1941年Rarita和Schwinger关于自旋为半整数的粒子理论的著名论文之后，我们提出了一个与自旋为3/2的粒子描述相关的表象空间的{ \em ab initio}构造。所选择的自旋为3/2的例子表明，波动方程的协方差以及附加条件的协方差本身并不足以保证框架与相对论的相容性--这是Velo和Zwanziger已经得到的教训。在这里，同样的教训在表征空间的层面上被证明是正确的，而不需要调用任何交互。详细的分析迫使我们放弃了单自旋解释的拉里塔和施温格框架，并提出了一个新的解释，充分尊重相对论。
Emergence of higher spin relativistic fermionic materials becomes a new favorite in the study of condensed matter physics. Massive Rarita-Schwinger 3/2-spinor was known owning very exotic properties, such as the superluminal fermionic modes and even being unstable in an external magnetic field. Due to the superluminal modes and the non-trivial constraints on the Rarita-Schwinger gas, we exposit anomalous properties of the Hall effects in (2+1)-dimensions which subvert the well-known quantum Hall paradigms. First, the Hall conductance of a pure Rarita-Schwinger gas is step-like but not plateau-…
In earlier work we introduced an abelianized gauge field model in which a Rarita-Schwinger field is directly coupled to a spin-$\frac{1}{2}$ field, and showed that this model admits a perturbative expansion in the gauge field coupling. As a preliminary to further study of the coupled model, in this paper we present a detailed analysis of the free field structure that obtains when the dimensionless gauge coupling is set to zero, but the dimension one coupling of the spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ fields remains nonzero.
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 $μ^2$ and $T^2$ are proporti…
We give a detailed analysis of an abelianized gauge field model in which a Rarita-Schwinger spin-$\frac{3}{2}$ field is directly coupled to a spin-$\frac{1}{2}$ field. The model permits a perturbative expansion in powers of the gauge field coupling, and from the Feynman rules for the model we calculate the chiral anomaly.
We study for the first time the effects of strong short-range electron-electron interactions in generic Rarita--Schwinger--Weyl semimetals hosting spin-3/2 electrons with linear dispersion at a four-fold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a $\math…
