Spin-3/2 fields in flat space-time

The equations for the spin-3/2 (Rarita-Schwinger) field given by linearized simple supergravity are written in space-plus-time form in terms ofSU(2) spinors, assuming that the background space-time is flat. Some consequences of these equations are analyzed and a Hamiltonian structure for the Rarita-Schwinger field is obtained.     

Note on the massive Rarita-Schwinger field in the AdS/CFT correspondence

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.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

Debye Potentials for Self-Dual Fields

It is shown that in a space-time that admits ageodetic and shear-free null vector field which is aprincipal direction of the conformal curvature(therefore, in any algebraically special solution of the Einstein vacuum field equations), any self-dualelectromagnetic field is locally given by a scalar(Debye) potential which obeys a second-orderdifferential equation and, similarly, that any self-dualYang-Mills field is locally given by a matrix-valuedpotential governed by a nonlinear second-orderdifferential equation. Using the fact that any self-dualelectromagnetic field is the self-dual part of a realsolution of the source-free Maxwell equations, it isshown that in any space-time of this class, the solutionof the source-free Maxwell equations is locally given bya Debye potential.     

Quantum Inequality Bounds for Free Rarita-Schwinger Field in Flat Spacetime

Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality (QEI), in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time.Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.     

Toward a theory of particles with 3/2 spin

A detailed analysis is performed of the pattern of meshes of irreducible Lorentz group representations corresponding to the direct product of vector and bispinor representations within the framework of the Gel'fand-Yaglom approach, for the purpose of determining the possibility of constructing various relativistic wave equations describing particles with a maximum spin of 3/2. Two such new equations are constructed for a 3/2 spin, which differ from the generally known Rarita-Schwinger and Fierz-Pauli equations. The nonequivalence of the latter is also proven.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–95, January, 1985.     

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. PACS numbers: 03.65.Pm; 04.20.Cv; 04.20.Fy.     

Rarita-Schwinger field: Dressing procedure and spin-parity of components

A general form of the total nonrenormalized propagator for a massive Rarita-Schwinger field is obtained with allowance for all spin components. The dressing of two opposite-parity Dirac fermions in the presence of mutual transitions is the closest analogy of dressing in the s = 1/2 sector of the Rarita-Schwinger field. A calculation of self-energy contributions confirms that the Rarita-Schwinger field involves, in addition to a leading component of spin s = 3/2, two opposite-parity components of spin s = 1/2.     

On the quantization of the axial current for the massless Rarita-Schwinger field

The chiral charge of the extra ghost needed for the quantization of the massless Rarita-Schwinger field is shown to have the opposite sign of that of the other ghosts and of the Rarita-Schwinger field itself. The effects of the gauge non-invariance on the quantum level of the classical axial current are discussed.     

Feynman propagator for a particle with arbitrary spin

Based on the solution to the Rarita-Schwinger equations, a direct derivation of the projection operator and propagator for a particle with arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin; the general commutation rules and Feynman propagator for a free particle of any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, 4 are provided.Received: 13 March 2003, Revised: 24 April 2005, Published online: 6 July 2005     

Ghost counting in supergravity

The elimination of unphysical degrees of freedom from a quantized massless Rarita-Schwinger field interacting with a (quantized or classical) gravitational field is analyzed on the one-loop level. It is shown that, beside the ordinary Faddeev-Popov ghosts, an extra ghost is needed to remove the effects of unphysical modes. The new ghost only couples to the S-matrix if the gauge-fixing of the Rarita-Schwinger field involves the gravitational field, but it is necessary in the partition function for other gauge choices.     

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearised Yang-Mills theory and linearised general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearised pure $N=1$ supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.     

Rarita-schwinger field and multicomponent wave equation

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

Statistical-Mechanical Entropies of Schwarzschild Black Hole due to Arbitrary Spin Fields in Different Coordinates

The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevg and Lemaitre coordinates. Although the metrics in the Painlevg and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevd and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.     

The Weak Energy Condition and Singularities in Classical Free N = 1 Supergravity

With the use of the modification of the weak energy condition for theories with torsion developed by Hehl, we analyse classical free N = 1 supergravity in the hope that spin-spin contact interactions may avert singularities, as happens in the neutrinic case. We find that this does not happen, since the appearence of singularities is conditioned by the cosmological model of the gravitino field in consideration. We present a very simple singularity free model for a spatially homogeneous Rarita-Schwinger field in a Robertson-Walker spacetime.     

弯曲时空的半整数自旋场方程

在弯曲时空中证明了γ-代数,并在切空间中写下Rarita-Schwinger场方程。基于等效原理,求得了弯曲时空中的Rarita-Schwinger场方程。 关键词：     

Molecular Force Fields of XY6 Type Molecules

Octahedral molecules of XY₆ type belonging to O_h symmetry have six normal modes of vibrations. On group theoretical considerations, Λ_vib, = a^1g + e_g + 2t_1u + t_2g + t_2u     

The Minimal Cqupling of Charged spin-3/2 Fields to an Extended Abelian Gauge Model

Charged spin-3/2 fields are coupled to an extended gauge model without the total suppression of the vector degrees of freedom which usually takes place as a consequence of simultaneously imposing the Maxwell and Rarita-Schwinger U(1) symmetries.