Rarita-Schwinger Field Research Articles

Rarita-Schwinger Quantum Free Field via Deformation Quantization

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.

Rarita-schwinger field and multicomponent wave equation

We suggest simple method to solve wave equation for Rarita--Schwinger field without additional constraints. This method based on use of off-shell projection operators allows to diagonalize spin-1/2 sector of the field.

“Dynamical” interactions and gauge invariance

Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge invariant and that gauge invariance and relativistic invariance stand on equal footings. A "dynamical" non-minimal interaction is constructed explicitly and the Rarita-Schwinger equation is considered in the framework of this "dynamical" interaction.

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.

Heavy-particle formalism with Foldy-Wouthuysen representation

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.

Symmetries of higher-spin fields and the electromagneticN→N*(1680)form factors

We study the Q^2-evolution of the form factors (FFs) for the nucleon-to-N(1680) transition in the framework of an effective field theory. To this end, the intrinsic symmetries of the spin-5/2 Rarita-Schwinger (RS) fields are analyzed, and a Lagrangian of the electromagnetic N-N(1680) interactions is constructed. The Lagrangian preserves all the intrinsic symmetries of the spin-5/2 field--point and gauge invariance--and does not involve lower-spin components of the reducible RS field. Besides, the symmetries postulate the definitions of the Lagrangian FFs. These FFs are modeled as dispersionlike expansions in a vector-meson--dominance model. A good agreement with the experimental data is achieved.

A toy model for higher spin Dirac operators

This paper deals with the higher spin Dirac operator Q2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight \( (\tfrac{5} {2},\tfrac{3} {2},\tfrac{1} {2},...,\tfrac{1} {2}) \). This operator acts as a toy model for generalizations of the classical Rarita—Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.

Weyl's gauge invariance: Conformal geometry, spinors, supersymmetry, and interactions

We extend our program of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones for universes that are Einstein, but are novel in general backgrounds. They are generalizations of the gravitational couplings of a conformally improved scalar to fields with general scaling and tensor properties. The couplings we find are more general than just trivial ones following from a conformal compensating mechanism. In particular, in the setting where a scale gauge field (or dilaton) is included, masses correspond to Weyl weights of fields organized in “tractor” multiplets. Breitenlohner–Freedman bounds follow directly from reality of these weights. Moreover, massive, massless and partially massless theories are handled in a uniform framework. Also, bona fide Weyl invariant theories (invariant without coupling to scale) can be directly derived in this approach. The results are based on the tractor calculus approach to conformal geometry, in particular we show how to handle Fermi fields, supersymmetry and Killing spinors using tractor techniques. Another useful consequence of the construction is that it automatically produces the (anti-) de Sitter theories obtained by log-radial reduction of Minkowski theories in one higher dimension. Theories presented in detail include interacting scalars, spinors, Rarita–Schwinger fields, and the interacting Wess–Zumino model.

Spin3/2baryons and form factors in AdS/QCD

We study the 5D Rarita-Schwinger fields to describe spin $3/2$ baryons in AdS/QCD. We calculate the spectrum of spin $3/2$ baryons ($\ensuremath{\Delta}$ resonances) and their form factors, together with meson-baryon couplings from AdS/QCD. The transition form factors between $\ensuremath{\Delta}$ and nucleon are evaluated. Both pion and rho meson couplings have the same origin in the bulk and hence are unified. The numerical values for the meson-baryon transition couplings are roughly consistent with the values obtained from other methods. We also predict the numerical values of some new couplings associated with $\ensuremath{\Delta}$ resonances.

On-shell consistency of the Rarita-Schwinger field formulation

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 nonlinear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit \ensuremath{\Delta}(1232) isobar degrees of freedom are discussed.

Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-$3/2$ Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in ${\mathrm{AdS}}_{4}$. Linear Rarita-Schwinger fields in ${\mathrm{AdS}}_{d}$ are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0\ensuremath{\le}|m|<1/2{l}_{\mathrm{AdS}}$. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is ``renormalized'' accordingly with the action. We then use the results obtained for $|m|=1/{l}_{\mathrm{AdS}}$ to explore supersymmetric boundary conditions for $\mathcal{N}=1$ ${\mathrm{AdS}}_{4}$ supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in $d=4$ supergravity correspond to gauging the superconformal group of the three-dimensional CFT describing M2-branes, while $\mathcal{N}=1$ supersymmetric mixed boundary conditions couple the CFT to $\mathcal{N}=1$ superconformal topologically massive gravity.

Three-dimensional 𝒩 = 8 conformal supergravity and its coupling to BLG M2-branes

This paper is concerned with the problem of coupling the = 8 superconformal Bagger-Lambert-Gustavsson (BLG) theory to = 8 conformal supergravity in three dimensions. We start by constructing the on-shell = 8 conformal supergravity in three dimensions consisting of a Chern-Simons type term for each of the gauge fields: the spin connection, the SO(8) R-symmetry gauge field and the spin 3/2 Rarita-Schwinger (gravitino) field. We then proceed to couple this theory to the BLG theory. The final theory should have the same physical content, i.e., degrees of freedom, as the ordinary BLG theory. We discuss briefly the properties of this ``topologically gauged'' BLG theory and why this theory may be useful.

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.

THE RARITA–SCHWINGER FIELD: RENORMALIZATION AND PHENOMENOLOGY

We discuss renormalization of propagator of interacting Rarita–Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For nonleading 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+ p →π+p leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.

Field Equations of Arbitrary Spin in Space-time with Torsion

A two spinor lagrangian formulation of field equations for massive particle of arbitrary spin is proposed in a curved space-time with torsion. The interaction between fields and torsion is expressed by generalizing the situation of the Dirac equation. The resulting field equations are different (except for the spin-1/2 case) from those obtained by promoting the covariant derivatives of the torsion free equations to include torsion. The non linearity of the equations, that is induced by torsion, can be interpreted as a self-interaction of the particle. The spin-1 and spin-3/2 cases are studied with some details by translating into tensor form. There result the Proca and Rarita-Schwinger field equations with torsion, respectively.

No interactions for a collection of spin-two fields intermediated by a massive Rarita–Schwinger field

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, Poincaré 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 the presence of a massive Rarita–Schwinger field. The basic features of the couplings between a single Pauli–Fierz field and a massive Rarita–Schwinger field are also emphasized.

Quantum Inequality Bounds for Free Rarita–Schwinger Field inFlat Spacetime

Although quantum field theory allows the local energy densitynegative, it also places severe restrictions on the negativeenergy. One of the restrictions is the quantum energyinequality (QEI), in which the energy density is averaged overtime, or space, or over space and time. By now temporal QEIs havebeen established for various quantum fields, but less work hasbeen done for the spacetime quantum energy inequality. In thispaper we deal with the free Rarita–Schwinger field and present aquantum inequality bound on the energy density averaged over spaceand time. Comparison with the QEI for the Rarita–Schwinger fieldshows that the lower bound is the same with the QEI. At the sametime, we find the quantum inequality for the Rarita–Schwingerfield is weaker than those for the scalar and Dirac fields. Thisfact gives further support to the conjecture that the morefreedom the field has, the more easily the field displays negativeenergy density and the weaker the quantum inequality becomes.

QUASINORMAL FREQUENCIES OF THE RARITA–SCHWINGER FIELD IN REISSNER–NORDSTRÖM-ANTI-DE SITTER SPACE–TIME

We investigate the quasinormal modes (QNMs) of Rarita–Schwinger field perturbations of a Reissner–Nordström black hole in an asymptotically anti-de Sitter space–time. We find that both the real and imaginary parts of the fundamental quasinormal frequencies of the large black hole are the linear functions of the Hawking temperature. The slope of the lines increases as the charge increases, but the imaginary parts decrease as the charge increases. We show that the quasinormal frequencies become evenly spaced for high overtone number n and the spacings are related to the charge and mass of the black hole. We also find that the real parts of the QNMs increase and the imaginary parts decrease as the angular quantum number increases.

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).

Rarita–Schwinger fields in the half space†

This article deals with the Hardy space related to solutions of generalized Rarita–Schwinger operators in the ball and the half space. These operators generalize the Rarita–Schwinger operator for spin-fields to the case of functions taking values in irreducible representation spaces with weight. †Dedicated to Richard Delanghe on the occasion of his 65th birthday.