Gauge invariant Lagrangian construction for massive higher spin fermionic fields

We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincaré group with given spin as the operator constraints in auxiliary Fock space, we built the BRST charge for the model under consideration and find the gauge invariant equations of motion in terms of vectors and operators in the Fock space. It is shown that like in massless case [I.L. Buchbinder, V.A. Krykhtin, A. Pashnev, Nucl. Phys. B 711 (2005) 367, hep-th/0410215], the massive fermionic higher spin field models are the reducible gauge theories and the order of reducibility grows with the value of spin. In compare with all previous approaches, no off-shell constraints on the fields and the gauge parameters are imposed from the very beginning, all correct constraints emerge automatically as the consequences of the equations of motion. As an example, we derive a gauge invariant Lagrangian for massive spin 3/2 field.     

Spin 2 Field Equation in Expanding Universe

The spin 2 field equations are separated in the Robertson-Walker space-time by the Newman-Penrose formalism and by using a null tetrad frame previously considered. The angular and radial separated equations are integrated by generalizing and improving results relative to the massless case. The separated time equations are governed by two coupled linear differential equations that depend on the cosmological background. They are solved and studied for some models of cosmological expansion such as the linear and exponential expansion and the matter dominated and radiative expansion of the standard cosmology.     

Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

The solution of Dirac's equation in algebraically special space-times

A procedure for obtaining solutions to Dirac's equation in algebraically special space-times which admit a shear-free congruence of null geodesies along the repeated principal null direction of the Weyl tensor, is presented. By aligning one of the Dirac spinors to the congruence the problem is reduced to solving one second-order linear partial differential equation for a scalar potential. The solution of the massless field equations for null fields of arbitrary spin s>1/2 aligned to the congruence is also given.     

Wave functions in geometric quantization

A geometrical way is described to associate quantum states in the sense of geometric quantization to wave functions in the quantum mechanical sense for each relativistic elementary particle. Explicit computations are made in a number of cases: Klein-Gordon and Dirac equations, neutrino and antineutrino Weyl equations, and very general cases of massive and massless particles of arbitrary spin. In this later case one is led in a canonical way to Penrose wave equations.     

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     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory II

In arXiv:1202.4298 gauge invariant interacting equations were written down for the spin 2 and spin 3 massive modes using the exact renormalization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant “field strengths” and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invariant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher-dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space–time and this is also outlined.     

Projection Operator and Feynman Propagator for a Free MassiVe Particle of Arbitrary Spin

Based on the solution to the Bargmann-Wigner equations, a direct derivation of the projection operator and Feynman propagator for a free massive particle of 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 with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.     

平面对称标量场的静态时空

本文求出零质量标量场产生的平面对称度规的静态通解,并研究了它的对称性、奇异性等整体特性,发现平面对称情况与球对称不同,标量场的引入与否,其时空的奇异性没有本质差别。 关键词：     

Calculating Debye potentials from data on ℐ or ℋ

Using the formalism of Cohen and Kegeles equations are obtained for arbitrary spin radiation field Debye potentials in Reissner-Nordström geometries, and a formal series solution is presented. For the case of integer spin the series is modified to what appears to be a more natural form. In the particular case of vanishing spin it is shown that in some important cases the modified series converges to a solution of the Debye potential equation, which is the scalar wave equation, and is simply related to characteristic initial data given on either H orI.     

QUANTIZATION OF THE PHOTON FIELD AND DIPOLE GHOSTS

We discuss the quantization of a massless vector field using the Lagrange mul-tiplier method. The exact solution of the field equations in three dimensional mo-mentum space is given and the existence of dipole ghosts explicitly demonstrated.One of the ghosts is not an eigenstate of the Hamiltonian and can be eliminated byboundary conditions. If the vector field is coupled to conserved currents, the otherghost has no observable effects. So this field theory describes the photon. This pro-blem has been studied by Nakanishi, but his analysis is obscure. The extension ofthis method to spin 3/2 massless field is discussed.     

Separation of Spin 0, 1/2, 1 Field Equations in Lemaître-Tolman-Bondi Cosmological Model with Cosmological Constant

The problem of variable separation of the scalar field equation is approached within the Lemaître-Tolman-Bondi (LTB) cosmological model with cosmological constant Λ. Parametric solutions of the cosmological Newton-like equation of the model are preliminary determined that result factorized in the parameter and in the radial dependence. The result holds on a sufficient condition that relates the two arbitrary integration functions of the model. The condition is of the same type of the one that ensures, in absence of cosmological term, the separability of the spin field equations for spin 0, 1/2, 1. It is then shown that the scalar field equation results automatically separable in the class of LTB models determined. The separated radial equation results independent of Λ, while the separated time equation strictly depends on Λ. The separability of the field equations is then checked to hold, in the same context, for spinor field equation of spin 1/2 and spin 1.     

Kerr时空中任意自旋的统一场方程的退耦和分离变量

通过微扰与退耦计算得到,在Kerr时空中对于静止质量为零、自旋为任意值的粒子场,所有场分量都能退耦,再采用Kinnersley零标架证明:只有中微子场的两个分量和电磁场的两个分量可以分离变量。     

Analysis of the wave functions for accelerating Kerr-Newman metric

As is well-known, it is very difficult to solve wave equations in curved space-time. In this paper,we find that wave equations describing massless fields of the spins s≤2 in accelerating KerrNewman black holes can be written as a compact master equation. The master equation can be separated to radial and angular equations, and both can be transformed to Heun's equation,which shows that there are analytic solutions for all the wave equations of massless spin fields.The results not only demonstrate that it is possible to study the similarity between waves of gravitational and other massless spin fields, but also it can deal with other astrophysical applications, such as quasinormal modes, scattering, stability, etc. In addition, we also derive approximate solutions of the radial equation.     

Non-equivalence between Heisenberg XXZ spin chain and Thirring model

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the antiferromagnetic case. We examine the relation between the XXZ spin chain and the massless Thirring model, and show that the spectrum of the XXZ spin chain has a gapless excitation while the regularized Thirring model calculated with the Bogoliubov transformation method has a finite gap. This finite gap spectrum is also confirmed by the Bethe ansatz solution of the massless Thirring model.Received: 28 October 2004, Published online: 21 January 2005PACS: 10.Kk, 03.70. + k, 11.30.-j, 11.30.Rd     

Explicit construction of conserved currents for massless fields of arbitrary spin

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s₁ field and two spin-s₂ fields. The class is restricted only to 2s₂⩽s₁. In case s₁ = 4 and s₂ = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.     

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.