A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s>0 in four dimensional flat spacetime. These results generalize the recent classification in the spin s=1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s>0 analogs of the well-known electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a spin s>0 analog of a novel chiral tensor found in the spin s=1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e., a phase rotation) on the spin s field, in contrast to the even parity of the stress-energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s>0 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated to the stress-energy, zilch, and chiral tensors, and higher derivative extensions of these currents in which the spin s field is replaced by its repeated conformally-weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct, unified characterization in terms of Killing spinors. The cases s=2, s=1/2 and s=3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.
We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,\mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1\geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.
This thesis presents the general structure of non-conformal higher-spin supercurrent multiplets in three and four spacetime dimensions. Such supercurrents are in one-to-one correspondence with off-shell massless higher-spin gauge supermultiplets, some of which are constructed in this thesis for the first time. In the first part of the thesis, we propose a new off-shell formulation for a massless integer superspin multiplet, whose gauge-invariant action involves an unconstrained complex superconformal prepotential, in conjunction with two types of compensators. Next, we deduce the structure of …
A natural presymplectic structure for non-Lagrangian equations of motion governing the dynamics of free higher-spin fields in four-dimensional anti-de Sitter space is proposed. This presymplectic structure is then used to the derivation of the conserved currents associated with the relativistic invariance and to the construction of local functionals of fields that are gauge invariant on shell.
We investigate cubic interactions between a chiral superfield and higher spin superfield corresponding to irreducible representations of the $4D,\, \mathcal{N}=1$ super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether's method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets $(s+1,s+1/2)$…
Recently found spin-flip non-invariant (SFNI) conserved quantities play important roles in discussing nonequilibrium physics of the XXZ model. The representative examples are the generalized Gibbs ensemble (GGE) and the ballistic transport of the spin current. In spite of big progress in understanding nonequilibrium physics of integrable systems, the general framework to determine a minimal complete set of conserved quantities which describes the long-time steady state has not yet been found. This paper shows that the GGE of the gapless XXZ model consists of functionally independent conserved …
In the early 80's, R. Rüdiger published a pair of articles in which it was found the most general conserved charges associated to the motion of particles with spin moving in curved spacetime. In particular, it was shown that besides the well-known conserved quantity associated to Killing vectors, it is also possible to have another conserved quantity that is linear in the spin of the particle if the spacetime admits a Killing-Yano tensor. However, in these papers it was proved that in order for this new scalar to be conserved two obscure conditions involving the Killing-Yano tensor and the cur…
We present a rigorous explicit expression for an extensive number of local conserved quantities in the XYZ spin-1/2 chain with general coupling constants. All the coefficients of operators in each local conserved quantity are calculated. We also confirm that our result can be applied to the case of the XXZ chain with a magnetic field in the z-axis direction.
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin 1/2 chain and rigorously establish their linear independence from the well-known set of local conserved charges.
We consider the isotropic spin-$1/2$ Heisenberg spin chain weakly perturbed by a local translationally- and $SU(2)$-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation the quasi-conserved quantities indeed exist, and we construct an explicit form for the first f…
In four dimensions, partially massless fields of all spins and depths possess a duality invariance akin to electric-magnetic duality. We construct metric-like gauge invariant curvature tensors for partially massless fields of all integer spins and depths, and show how the partially massless equations of motion can be recovered from first order field equations and Bianchi identities for these curvatures. This formulation displays duality in its manifestly local and covariant form, in which it acts to interchange the field equations and Bianchi identities.
We study the linear response of a spin current to a small electric field in a two-dimensional crystalline insulator with non-conserved spin. We adopt the spin current operator proposed in [J. Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], which satisfies a continuity equation and fits the Onsager relations. We use the time-independent perturbation theory to present a formula for the spin Hall conductivity, which consists of a "Chern-like" term, reminiscent of the Kubo formula obtained for the quantum Hall systems, and a correction term that accounts for the non-conservation of spin. We illus…
We extend T. Prosen's construction of quasilocal conserved quantities for the XXZ model [Phys. Rev. Lett. 106, 217206 (2011)] to the case of periodic boundary conditions. These quasilocal operators stem from a two-parameter transfer matrix which employs a highest-weight representation of the quantum group algebra inherent in the Yang-Baxter algebra. In contrast with the open chain, where the conservation law is weakly violated by boundary terms, the quasilocal operators in the periodic chain exactly commute with the Hamiltonian and other local conserved quantities.
We study the massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space. The Casimir operators are constructed and their eigenvalues are found. It is shown that the finite spin (helicity) representation is defined by two integer or half-integer numbers while the infinite spin representation is defined by the real parameter $μ^2$ and one integer or half-integer number.
We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin $1$ and $2$. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved…
