Sudip Karan, Shashank Kumar, Binata Panda
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.
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The Rarita-Schwinger equations are generalised for the delta baryon having spin 3/2 and isospin 3/2. The coupling of the nucleon and the delta fields is studied. A possible generalisation of the Walecka model is proposed.
We consider a massive Rarita-Schwinger field on the Anti-de Sitter space and solve the corresponding equations of motion. We show that appropriate boundary terms calculated on-shell give two-point correlation functions for spin-3/2 fields of the conformal field theory on the boundary. The relation between Rarita-Schwinger field masses and conformal dimensions of corresponding operators is established.
In this paper, we establish basic material for future investigations of the analysis and geometry of the twistor bundle, and of differential operators with the twistor bundle as source and/or target, especially the Rarita-Schwinger operator, a first order differential operator taking twistors to twistors.
A free Rarita-Schwinger field in the Anti-de Sitter space is considered. We show that the usual action can be supplemented by a boundary term that can be interpreted as the generating functional of the correlation functions in a conformal field theory on the boundary of the Anti-de Sitter space.
We provide a gauge covariant formalism of the canonically quantized theory of spin-3/2 Rarita-Schwinger gauge field. The theory admits a quantum gauge transformation by which we can shift the gauge fixing parameter. The quantum gauge transformation does not change the BRST charge. Thus, the physical Hilbert space is trivially independent of the gauge fixing parameter.
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields a consistent classical theory, with a generalized fermionic gauge invariance realized as a canonical transformation. 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 …
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.
Anomaly Inflow of Rarita-Schwinger Field in 3 Dimensions
该研究探讨3维带规范对称性的Rarita-Schwinger场反常流入，通过谱流分析证实其反常可由反常流入刻画，还得到不同流形下的整体反常存在性与配分函数反常相位结果。
The complete solution to the massive Rarita-Schwinger field equation in anti-de Sitter space is constructed, and used in the AdS/CFT correspondence to calculate the correlators for the boundary conformal field theory. It is found that when no condition is imposed on the field solution, there appear two different boundary conformal field operators, one coupling to a Rarita-Schwinger field and the other to a Dirac field. These two operators are seen to have different scaling dimensions, with that of the spinor-coupled operator exhibiting non-analytic mass dependence.
The cross-couplings among several massless spin-two fields (described in the free limit by a sum of Pauli-Fierz actions) in the presence of a massive Rarita-Schwinger field are investigated in the framework of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, Lorentz covariance, and the preservation of the number of derivatives on each field, we prove that there are no consistent cross-interactions among different gravitons with a positively defined metric in internal space in t…
Rarita-Schwinger model in Very Special Relativity
本文在非常相对论框架下研究了Rarita-Schwinger模型中的真空极化，探讨了与Maxwell场耦合的自旋3/2场，并采用Mandelstam-Leibbrandt预设进行一阶积分计算。
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…
Bhabha-like scattering in the Rarita-Schwinger model at finite temperature
本文在有限温度下利用热场动力学形式，在树图层次计算有质量Rarita-Schwinger模型中费米子-反费米子散射的截面，以研究温度效应对类Bhabha散射的影响。
In this letter the boundary problem for massless and massive Rarita-Schwinger field in the AdS/CFT correspondence is considered. The considerations are along the lines of a paper by Henneaux (hep-th/9902137) and are based on the requirement the solutions to be a stationary point for the action functional. It is shown that this requirement, along with a definite asymptotic behavior of the solutions, fixes the boundary term that must be added to the initial Rarita-Schwinger action. It is also shown that the boundary term reproduce the known two point correlation functions of certain local operat…
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…
On the photon mass generation in Rarita-Schwinger QED
该研究针对2、3维时空下的Rarita-Schwinger QED，通过分析单圈阶1PI函数主导项与光子传播子极点结构，探究Rarita-Schwinger场对光子动力学质量生成的影响，并讨论了模型的可重整化性。
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…
Carroll-Field-Jackiw term in a massless Rarita-Schwinger model
本研究针对无质量Rarita-Schwinger的LV QED，引入规范固定得到RS场传播子并计算Carroll-Field-Jackiw项，发现其有限且有歧义，仅在基于非线性规范框架的计算方案中结果具有规范无关性。
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 n…
We study quantization of a minimally gauged massless Rarita-Schwinger field, by both Dirac bracket and functional integral methods. The Dirac bracket approach in covariant radiation gauge leads to an anticommutator that has a non-singular limit as gauge fields approach zero, is manifestly positive semidefinite, and is Lorentz invariant. The constraints also have the form needed to apply the Faddeev-Popov method for deriving a functional integral, using the same constrained Hamiltonian and inverse constraint matrix that appear in the Dirac bracket approach.
Rarita-Schwinger equation from principle equation for all spins
本文在Casimir本征值方程原理框架下，从全自旋原理方程导出有质量自旋-3/2的Rarita-Schwinger方程，并证明矢量-旋量场包含两个自旋-1/2 Dirac场。
We derive the most general lagrangian of the free massive Rarita--Schwinger field, which generalizes the previously known ones. The special role of the reparameterization transformation is discussed.
We consider the electromagnetic and gravitational interactions of a massive Rarita-Schwinger field. Stueckelberg analysis of the system, when coupled to electromagnetism in flat space or to gravity, reveals in either case that the effective field theory has a model-independent upper bound on its UV cutoff, which is finite but parametrically larger than the particle's mass. It is the helicity-1/2 mode that becomes strongly coupled at the cutoff scale. If the interactions are inconsistent, the same mode becomes a telltale sign of pathologies. Alternatively, consistent interactions are those that…
Fermion-fermion scattering in a Rarita-Schwinger model with Yukawa-like interaction
研究了在拉里-施维林格模型中通过类似杨-米尔斯耦合介导的自旋-3/2费米子散射，分析了零温与有限温下的散射截面及短程与长程极限下的行为。
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 $5$…
Non-Abelian Carroll-Field-Jackiw term term in a Rarita-Schwinger model
本文证明在非阿贝尔规范场与自旋-3/2场耦合且存在恒定轴向矢量场时，可生成非阿贝尔 CFJ 项，并证明其有限且含歧义，在 't Hooft-Veltman 方案中消失。
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…
We obtain in analytical form the dressed propagator of the Rarita-Schwinger field taking into account all spin components and discuss shortly its properties.
Massless Rarita-Schwinger equations: Half and three halves spin solution
本研究用Behrends-Fronsdal投影算符重析无质量Rarita-Schwinger理论自由度，证实其规范不变部分含1/2和3/2自旋解，质疑剩余规范对称性的根本依据，明确扩展哈密顿动力学消除1/2自旋模式需以Dirac猜想为前提且无法准确描述原拉格朗日系统。
Lorentz-breaking Rarita-Schwinger model
本文构造了自旋-3/2场的洛伦兹破缺扩展并耦合到阿贝尔规范场，计算了有限但歧义的CFJ项、高阶导数CFJ项以及二阶LV矢量的aether项。
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 obtain in analytical form the dressed propagator of the massive Rarita-Schwinger field taking into account all spin components. We found that the nearest analogy for dressing the Rarita--Schwinger field in spin--1/2 sector is dressing the two Dirac fermions of opposite parity with presence of mutual transitions. The calculation of the self-energy contributions confirms that besides the leading spin--3/2 component the Rarita--Schwinger field contains also two spin--1/2 components of different parity.
Nonlocal Rarita-Schwinger theory
本文构建了自旋-3/2 费米子的非局域 Rarita-Schwinger 理论，考虑两类解析形状因子，证明自由约束不变且无鬼影，并给出传播子与色散关系。
Dressing fields for supersymmetry: The cases of the Rarita-Schwinger and gravitino fields
该研究指出刚性超对称场论和超引力中提取Rarita-Schwinger场与引力微子场离壳自由度的规范固定条件属于修饰场方法实例，求解约束可将二者实现为非定域关系变量，是该方法首次应用于超对称理论。
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) …
The heat kernel for the spin-3/2 Rarita-Schwinger gauge field on an arbitrary Ricci flat space-time ($d>2$) is investigated in a family of covariant gauges with one gauge parameter $α$. The $α$-dependent term of the kernel is expressed by the spin-1/2 heat kernel. It is shown that the axial anomaly and the one-loop divegence of the action are $α$-independent, and that the conformal anomaly has an $α$-dependent total derivative term in $d=2m\geq6$ dimensions.
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…
In this work, we calculate the solutions of the Rarita-Schwinger equation with the inclusion of the eletromagnetic interaction. Our gauge and coupling prescription choices lead to Dirac-type solutions. One of the consequences of our results are the Landau level occupation of particles, quite different from the usual spin 1/2 particle system occupation numbers.
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.
On the spin content of the classical massless Rarita--Schwinger system
本文分析经典无质量 Rarita--Schwinger 系统的自旋内容，在拉格朗日与哈密顿框架下研究规范固定与 Dirac 猜想对自旋-1/2 和自旋-3/2 传播的影响，揭示了不同约束处理下的理论差异。
We propose a relativistic Jeff=3/2 semimetal with 4d1 or 5d1 electrons on a cubic lattice when the strong spin-orbital coupling takes over the Hunds' coupling. A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. In the massless case, the right- and left-handed chiral degrees of freedom of the Rarita-Schwinger spinors are independent. In the lattice model that we propose, the right- and left- handed gapless points in Brillouin zone are separated. We call this linearly dispersed semimetal Rarita-Schwinger-Weyl semimetal, similar to Weyl semimetal for spin 1/2 syst…
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 …
Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequa…
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…
We employ the two independent Casimir operators of the Poincare group, the squared four--momentum, P^2, and the squared Pauli-Lubanski vector, W^2, in the construction of a covariant mass-m, and spin-3/2 projector in the four-vector-spinor, ψ_μ. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin-3/2} particle coupled to the electromagnetic field by a gyromagnetic ratio of g_{3/2}=2.
We discuss the semiclassical scattering problem for massless matter coupled to Rarita-Schwinger field in four dimensional Minkowski space. We rewrite the soft gravitino theorem as a Ward identity for the S-matrix and discuss the relationship of corresponding symmetry charges to new asymptotic fermonic symmetries of massless Rarita-Schwinger field.
After a brief review of the celebrated 1941 paper of Rarita and Schwinger on the theory of particles with half-integral spins, we present an {\em ab initio} construct of the representation space relevant for the description of spin-3/2 particles. The chosen example case of spin-3/2 shows that covariance of a wave equation, and that of the imposed supplementary conditions, alone is not a sufficient criterion to guarantee the compatibility of a framework with relativity -- a lesson already arrived by Velo and Zwanziger. Here this same lesson is shown to be true at the level of the representation…
Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the deformation quantization formalism, in relation to the Dirac field case. This happens because the vector structure of the RS field imposes constraints on the space of wave function solutions and not on the operator structure. The RS propagator was also calculated within this formalism.
We prove that any bilinear coupling of a massive spin-3/2 field can be brought into a gauge invariant form suggested by Pascalutsa by means of a non-linear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit Delta (1232) isobar degrees of freedom are discussed.
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-…
We discuss renormalization of propagator of interacting Rarita--Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For non-leading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of $Δ^{++}(1232)$ in $π^{+}\particle{p}\to π^{+}\particle{p}$ leads to good description of total cross-section and to reasonable agreement with results of…
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 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 prop…
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…
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 quantisation 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 11d SUGRA and 4d, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formula…
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