Half-integer Spin Fields Research Articles

Quasinormal modes for integer and half-integer spins within the large angular momentum limit

While independent observations have been made regarding the behaviour of effective quasinormal mode (QNM) potentials within the large angular momentum limit, we demonstrate analytically here that a uniform expression emerges for non-rotating, higher-dimensional, and spherically-symmetric black holes (BHs) in this regime for fields of integer and half-integer spin in asymptotically flat and dS BH contexts; a second uniform expression arises for these QNM potentials in AdS BH spacetimes. We then proceed with a numerical analysis based on the multipolar expansion method recently proposed by Dolan and Ottewill to determine the behaviour of quasinormal frequencies (QNF) for varying BH parameters in the eikonal limit. We perform a complete study of Dolan and Ottewill's method for perturbations of spin $s \in \{0,1/2,1,3/2,2 \}$ in 4D Schwarzschild, Reissner-Nordstr{\"o}m, and Schwarzschild de Sitter spacetimes, clarifying expressions and presenting expansions and results to higher orders $(\mathcal{O}(L^{-6}))$ than many of those presented in the literature $(\sim \mathcal{O}(L^{-2}))$. We find good agreement with known results of QNFs for low-lying modes; in the large-$\ell$ regime, our results are highly consistent with those of Konoplya's 6th-order WKB method. We confirm a universality in the trends of physical features recorded in the literature for the low-lying QNFs (that the real part grows indefinitely, the imaginary tends to a constant as $\ell \rightarrow \infty$, etc.) as we approach large values of $\ell$ within these spacetimes, and explore the consequent interplay between BH parameters and QNFs in the eikonal limit.

Cubic interactions of arbitrary spin fields in 3d flat space

Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and spin one-half) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic interaction vertices which we refer to as first-derivative form and higher-derivative form. All cubic interaction vertices are built by using the first-derivative form.

Towards Lagrangian construction for infinite half-integer spin field

We formulate the conditions for the generalized fields in the space with additional commuting Weyl spinor coordinates which define the infinite half-integer spin representation of the four-dimensional Poincaré group. Using this formulation we develop the BRST approach and derive the Lagrangian for the half-integer infinite spin fields.

Asymptotically flat structure of hypergravity in three spacetime dimensions

The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-$5/2$ field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS$_{3}$. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W$_{\left(2,4\right)}$ algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined "Killing vector-spinors". The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or anti-periodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree $s+\frac{1}{2}$ in the energy, where $s$ is the spin of the fermionic generators.

A spectral method for half-integer spin fields based on spin-weighted spherical harmonics

We present a new spectral scheme for analysing functions of half-integer spin-weight on the two-sphere and demonstrate the stability and convergence properties of our implementation. The dynamical evolution of the Dirac equation on a manifold with spatial topology of with a pseudo-spectral method is also demonstrated.

Higher spin fermions in the BTZ black hole

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant in terms of the quasinormal modes and show it agrees with that obtained by integrating the heat kernel found by group theoretic methods.

Half-integer higher spin fields in (A)dS from spinning particle models

We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose curvatures are computed with the present models, are spinor-tensors of mixed symmetry corresponding to Young tableaux with D/2 - 1 rows and r columns, thus reducing to totally symmetric spinor-tensors in four dimensions. The paper generalizes similar results obtained in the context of integer spins in (A)dS.

Dirac quasinormal modes of D-dimensional de Sitter spacetime

We find exact solutions to the Dirac equation in D-dimensional de Sitter spacetime. Using these solutions we analytically calculate the de Sitter quasinormal (QN) frequencies of the Dirac field. For the massive Dirac field this computation is similar to that previously published for massive fields of half-integer spin moving in four dimensions. However to calculate the QN frequencies of the massless Dirac field we must use distinct methods in odd and even dimensions, therefore the computation is different from that already known for other massless fields of integer spin.

Massive relativistic particle models with bosonic counterpart of supersymmetry

We consider the massive relativistic particle models on four-dimensional Minkowski space extended by N commuting Weyl spinors for N=1 and N=2. The N=1 model is invariant under the most general form of bosonic counterpart of simple D=4 supersymmetry, and provides after quantization the bosonic counterpart of chiral superfields, satisfying Klein–Gordon equation. In massless case these fields do satisfy the Fierz–Pauli equations. For N=2 we obtain after quantization the free massive higher spin fields for arbitrary spin satisfying linear Bargman–Wigner equations. Finally, the problem of statistics in presented framework for half-integer classical spin fields is discussed.

On schizosymmetric superfields and $sl(2/1, \Bbb{ C})_\Bbb{R}$ supersymmetry

Superfield expansions over four-dimensional graded spacetime (xµ,θν), with Minkowski coordinates x extended by vector Grassmann variables θ, are investigated. By appropriate identification of the physical Lorentz algebra in the even and odd parts of the superfield, a typology of `schizofields' containing both integer and half-integer spin fields is established. For two of these types, identified as `gauge potential'-like and `field strength'-like schizofields, an supersymmetry at the component field level is demonstrated. Prospects for a schizofield calculus, and application of these types of field to the particle spectrum, are adumbrated.

Absorption by extremal D3-branes

The absorption in the extremal D3-brane background is studied for a class of massless fields whose linear perturbations leave the ten-dimensional background metric unperturbed, as well as the minimally-coupled massive scalar. We find that various fields have the same absorption probability as that of the dilaton-axion system, which is given exactly via the Mathieu equation. We analyze the features of the absorption cross-sections in terms of effective Schr\"odinger potentials, conjecture a general form of the dual effective potentials, and provide explicit numerical results for the whole energy range. As expected, all partial-wave absorption probabilities tend to zero (one) at low (large) energies, and exhibit an oscillatory pattern as a function of energy. The equivalence of absorption probabilities for various modes has implications for the correlation functions on the field, including subleading contributions on the field-theory side. In particular, certain half-integer and integer spin fields have identical absorption probabilities, thus providing evidence that the corresponding operator pairs on the field theory side belong to the same supermultiplets.

Constructing classical and quantum superconformal algebras on the boundary of AdS

Motivated by recent progress on the correspondence between string theory on anti-de Sitter space and conformal field theory, we address the question of constructing space–time N extended superconformal algebras on the boundary of AdS 3 . Based on a free field realization of an affine SL(2|N/2) current superalgebra residing on the world sheet, we construct explicitly the Virasoro generators and the N supercurrents, N is even. The resulting superconformal algebra has an affine SL(N/2)⊗U(1) current algebra as an internal subalgebra. Though we do not complete the general superalgebra, we outline the underlying construction and present supporting evidence for its validity. Particular attention is paid to its BRST invariance. In the classical limit where the free field realization may be substituted by a differential operator realization, we discuss further classes of generators needed in the closure of the algebra. We find sets of half-integer spin fields, and for N≥6 these include generators of negative weights. An interesting property of the construction is that for N≠2 it treats the supercurrents in an asymmetric way. Thus, we are witnessing a new class of superconformal algebras not obtainable by conventional Hamiltonian reduction. The complete classical algebra is provided in the case N=4 and is of a new and asymmetric form.

The Coordinate-Independent 2-Component Spinor Formalism and the Conventionality of Simultaneity

In recent articles, Zangari (1994) and Karakostas (1997) observe that while an ε-extended version of the proper orthochronous Lorentz group O ↑ + (1,3) exists for values of ε not equal to zero, no similar ε-extended version of its double covering group SL(2, C) exists (where ε=1−2 ε R, with ε R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for such behaviour, ε-coordinate transformations for any value of ε≠0 are ruled out empirically. In this article, I make two observations: (a) There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields. (b) There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular. I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995).

MASSIVE FIELDS WITH ARBITRARY HALF-INTEGER SPIN IN CONSTANT ELECTROMAGNETIC FIELD

We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in the external field to an algebraic problem of search for a set of operators with certain algebraic features using the representation of the higher-spin fields as vectors in a pseudo-Hilbert space. We consider such construction at linear order in the external electromagnetic field and also present an explicit form of interaction Lagrangians and gauge transformations for the massive particles of spins [Formula: see text] and [Formula: see text] in terms of symmetric spin-tensor fields. The obtained result is valid for space–time of arbitrary even dimension.

NONLOCAL EXTENDED CONFORMAL ALGEBRAS ASSOCIATED WITH MULTICONSTRAINT KP HIERARCHY AND THEIR FREE FIELD REALIZATIONS

We study the conformal properties of the multiconstraint KP hierarchy and its non-standard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multiconstraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free field realizations of its associated nonlocal algebras.

R-Deformed Heisenberg Algebra, Anyons and D=2+1 Supersymmetry

A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d=2+1 supersymmetric field systems. Quadratic and linear forms of action functionals are found for the universal minimal as well as for supersymmetric spinor sets of equations. A possibility of constructing a universal classical mechanical model for d=2+1 spin systems is discussed.

R-DEFORMED HEISENBERG ALGEBRA

It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of para-Grassmann algebra with a special differentiation operator. Guon-like form of the algebra, related to the generalized statistics, is found. Some applications of revealed representations of the R-deformed Heisenberg algebra are discussed in the context of OSp(2|2) supersymmetry. It is shown that these representations can be employed for realizing (2+1)-dimensional supersymmetry. They also give a possibility to construct a universal spinor set of linear differential equations describing either fractional spin fields (anyons) or ordinary integer and half-integer spin fields in 2+1 dimensions.

General considerations of matter coupling with the self-dual connection

It has been shown for low-spin fields that the use of only the self-dual part of the connection as basic variable does not lead to extra conditions or inconsistencies. We study whether this is true for more general chiral action. We generalize the chiral gravitational action, and assume that half-integer spin fields are coupled with torsion linearly. The equation for torsion is solved and substituted back into the generalized chiral action, giving four-fermion contact terms. If these contact terms are complex, the imaginary part will give rise to extra conditions for the gravitational and matter field equations. We study the four-fermion contact terms taking spin-1/2 and spin-3/2 fields as examples.

Massive fields of arbitrary spin in curved space-times

A possibility to describe massive fields of spins≧1/2 within general relativity theory without auxiliary fields and subsidiary conditions is proposed. Using the 2-component spinor calculus the Lagrangian is given for arbitrarys in an uniform manner. The related Euler-Lagrange equations are the wave equations studied by Buchdahl and Wünsch. The results are specified for fields of integer and half-integer spin: A suitable generalization of Proca's equation and Lagrangian leads to an equivalent tensor description of bosonic fields, whereas a generalization of Dirac's theory allows an equivalent description of fermionic fields by use of bispinors. AU (1)-gauge invariance of the Lagrangian is obtained by coupling to an electrogmagnetic potential. The current vector of the spin-s field is derived.

Extended conformal algebras generated by a multiplet of primary fields

Extended conformal algebras generated by a single multiplet of primary fields of integer or half-integer spin are studied. Closed W-algebraic structures are obtained for a finite set of values of the central charge. For odd spin a series of algebras with SO(3) symmetry is found. They are present in the (1, q) Virasoro minimal models. A free field construction for these algebras is discussed.