Journal ArticleDOI
Riemann curvature scalar of spacetime tangent bundle
TLDR
In this paper, the authors derived a useful expression for the Riemann curvature scalar of the space-time tangent bundle manifold by working in an anholonomic basis adapted to the spacetime affine connection.Abstract:
The maximum possible proper acceleration relative to the vacuum determines much of the differential geometric structure of the space-time tangent bundle. By working in an anholonomic basis adapted to the spacetime affine connection, one derives a useful expression for the Riemann curvature scalar of the bundle manifold. The explicit documentation of the proof is important because of the central role of the curvature scalar in the formulation of an action with resulting field equations and associated solutions to physical problems.read more
Citations
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Finslerian Fields in the Spacetime Tangent Bundle
TL;DR: In this article, a variety of differential-geometric Finslerian fields are exposited, and the structure of FINsian quantum fields receives particular emphasis, and possible generalizedactions are proposed for FINSlerian strings and p-branes.
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Quantum Fields in the Spacetime Tangent Bundle
TL;DR: In this article, a maximal acceleration invariant quantum field is formulated in terms of the differential geometric structure of the spacetime tangent bundle, and the field is shown to have a physically based Planck-scale effective regularization and a spectral cutoff at the Planck mass.
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Complex spacetime tangent bundle
TL;DR: In this paper, it was shown that the spacetime tangent bundle is complex in the case of Finsler spacetime, provided that the gauge curvature field vanishes, and the conditions for the vanishing of the Nijenhuis tensor in the anholonomic frame adapted to spacetime connection.
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Finsler-spacetime tangent bundle
TL;DR: In this paper, the Levi-Civita connection coefficients of the spacetime tangent bundle, for the case of a Finsler spacetime, are reduced to the form given by Yano and Davies.
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Finslerian quantum fields and microcausality
TL;DR: In this article, a class of Finslerian quantum fields in Minkowski spacetime were studied and the necessary field commutators were shown to be vanishing, provided the adjoint field is consistently generalized and the field is micro-causal.
References
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Tangent and cotangent bundles
TL;DR: In this article, the authors consider the problem of finding an isomorphism in a set of subsets of a TM and show that there exists a neighborhood W 1, W 2, W 3 of (p, Xp), (p); F ( Xp) and F (Xp) respectively such that W 1 is an open set.
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TL;DR: In this article, the microcanonical density of states for a weakly interacting gas of strings compactified on a torus is computed in the limit of large energy, taking into account conservation of winding number and momentum.
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Maximal proper acceleration and the structure of spacetime
TL;DR: In this article, a limiting proper acceleration in nature follows deductively from known physics and compels the union of spacetime and four-velocity space into a maximal-acceleration invariant phase space having an intrinsic Kaluza-Klein-type fiber-bundle structure with manifest gauge properties.