Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math-ph/0612004

Noether identities in Einstein--Dirac theory and the Lie derivative of spinor fields

Marcella Palese·Ekkehart Winterroth
View original source ↗Read source document ↗Export metadata ↓

Abstract

We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restrictions on the Lie derivative of fields.

Explore related subjects

math-phhep-thmath.DGmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Marcella Palese, Ekkehart Winterroth. 2008-10-15. Noether identities in Einstein--Dirac theory and the Lie derivative of spinor fields. https://doi.org/10.1142/9789812790613_0054

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Two-parameter Littlewood identities and half-space Yang--Baxter random fields for stable spin Hall--Littlewood symmetric functions

We prove a two-parameter skew Littlewood identity for stable spin Hall--Littlewood symmetric functions, generalizing Warnaar's identity. This identity yields a half-space extension of the Yang--Baxter random field of Bufetov and Petrov. Using their stochastic Yang--Baxter move together with the skew Littlewood identity, we construct explicit bulk and boundary sampling rules and characterize the two boundary regimes in which these rules admit autonomous projections onto the first $R$ column lengths for every $R\ge1$. In these regimes, the partition-length fields agree, after explicit coordinate and parameter changes, with the half-space stochastic six-vertex model of Barraquand, Borodin, Corwin and Wheeler and a subfamily of He's model. The two-column projections retain spin dependence and converge, under the respective continuous-time scalings, to the same two-layer exclusion process whose first layer is open ASEP. We also prove that the joint distributions of partition lengths in ascending processes are independent of spin throughout the nonnegative parameter range. Using this spin independence and the distributional comparisons with half-space six-vertex heights, we transfer He's asymptotic results to diagonal partition lengths, obtaining Tracy--Widom GSE and GOE limits, Gaussian limits, and a GSE--GOE crossover under boundary tuning. The GOE limit also holds at the even-column specialization. Finally, the first-layer particle count of the continuous-time process has GOE fluctuations.

math-ph↗
arXiv2026

Topological Orders from Reflection Positive Frustration-free Hamiltonians

We establish a framework based on reflection positivity for analyzing topologically ordered quantum spin systems and reconstructing their boundary algebras. For any reflection positive frustration-free Hamiltonian, we prove that the local topological quantum order (LTQO) condition of ground states on a disk holds, if and only if the ground state on the sphere obtained by gluing the disk with its reflection is nondegenerate. Furthermore, we show that Osterwalder-Schrader reconstruction produces the local net of boundary operator algebras from the local ground states, offering a constructive approach to topological holography through spatial reflection positivity.

math-ph↗
arXiv2026

Borel Summability of the Spatial Gradient Expansion in Linear Kinetic Theory

The passage from kinetic theory to hydrodynamics proceeds through gradient expansions whose large-order behavior depends on the model and on whether the gradients are temporal or spatial. Known examples of divergent temporal gradient expansions include those arising in Bjorken flow in Müller-Israel-Stewart theory, where positive-axis Borel singularities obstruct ordinary Borel summation and require a transseries completion. By contrast, some spatial gradient expansions in holographic theories and relativistic kinetic theory converge within a finite radius. We show that the spatial Chapman-Enskog expansion of the linear one-dimensional BGK equation realizes a third possibility: its coefficients can be obtained in closed form at all orders, and the resulting series is factorially divergent yet Borel summable along the positive axis. The unambiguous Borel sum reconstructs the hydrodynamic dispersion branch up to its merger with the essential spectrum and provides its analytic continuation beyond that point. We trace the divergence of the spatial expansion to the unbounded velocity support of the Maxwellian equilibrium: replacing it with a compactly supported equilibrium removes the factorial growth and gives the series a nonzero radius of convergence.

math-ph↗