GRTensorII: A computer algebra system for general relativity

Musgrave, Peter; Pollney, Denis; Lake, Kayll

doi:10.1090/fic/015/42

Cited by 30 publications

(38 citation statements)

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“…Furthermore, we are honoured to thank Gary Gibbons, Stephen Hawking, Sven Moch, Diana Vaman and Peter van Nieuwenhuizen for discussions and are deeply indebted to Nigel Hitchin for providing us the derivation of the residues f (s + 1)/2 and f (s + 3)/2 required in the η invariant computation [36]. The calculations reported in this paper made extensive use of the tensor algebra package GRtensor [47] along with the algebraic manipulation program FORM [48].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Spinors on manifolds with boundary: APS index theorems with torsion

Peeters¹,

Waldron²

1999

J. High Energy Phys.

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Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS η invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mechanics representation. Here we find agreement with existing results which employed heat kernel and Pauli-Villars techniques. Nonetheless, this computation also provides a stringent check of the Feynman rules of de Boer et al. for the computation of quantum mechanical path integrals. Our results can be verified via a duality relation between manifolds admitting a Killing-Yano tensor and manifolds with torsion. As an explicit example, we compute the indices of Taub-NUT and its dual constructed using this method and find agreement for any finite radius to the boundary. We also suggest a resolution to the problematic appearance of the Nieh-Yan invariant multiplied by the regulator (mass) 2 in computations of the chiral gravitational anomaly coupled to torsion.

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Section: Acknowledgmentsmentioning

confidence: 99%

Spinors on manifolds with boundary: APS index theorems with torsion

Peeters¹,

Waldron²

1999

J. High Energy Phys.

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“…p is used for degree of fractional differentiation, the familiar non-fractional differential equations are recovered when p = 1, P, µ, U a are the pressure, density and co-moving vector of a fluid. Calculations were carried out using maple9/grtensorII [5].…”

Section: Outline and Conventionsmentioning

confidence: 99%

Fractional Derivative Cosmology

Roberts

2014

TPHY

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The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case and the field equations are nearly second order. For Robertson-Walker cosmology there is a simple fractional modification of the Friedman and conservation equations. In general fractional gravitational equations similar to Einstein's are hard to define as this requires fractional derivative geometry. What fractional derivative geometry might entail is briefly looked at and it turns out that even asking very simple questions in two dimensions leads to ambiguous or intractable results. A two dimensional line element which depends on the Gamma-function is looked at.

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“…We used the Maple commands sequence below for numerical integration of the system of equations (2,3). We use …”

Section: =Diff(phi(tau)tau)diff(te(tau)tau)=diff(t(tau)tau)four);mentioning

confidence: 99%