On Hypermomentum in General Relativity II. The Geometry of Spacetime

In Part I** of this series we have introduced the new notion of hypermomentum Δijk as a dynamical quantity characterizing classical matter fields. In Part II, as a preparation for a general relativistic field theory, we look for a geometry of spacetime which will allow for the accomodation of hypermomentum into general relativity. A general linearly connected spacetime with a metric (L4, g) is shown to be the appropriate geometrical framework

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On Hypermomentum in General Relativity I. The Notion of Hypermomentum

Zeitschrift für Naturforschung A ◽

10.1515/zna-1976-0201 ◽

1976 ◽

Vol 31 (2) ◽

pp. 111-114 ◽

Cited By ~ 6

Author(s):

Friedrich W. Hehl ◽

G. David Kerlick ◽

Paul von der Heyde

Keyword(s):

Field Theory ◽

General Relativity ◽

Angular Momentum ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Spin Angular Momentum ◽

Relativistic Field ◽

Rank Tensor ◽

General Relativistic ◽

Matter Fields

Abstract In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor ⊿ijk of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws.

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Relativistic Theory of the Non-symmetric Field

The Formative Years of Relativity ◽

10.23943/princeton/9780691174631.003.0023 ◽

2017 ◽

Author(s):

Hanoch Gutfreund ◽

Jürgen Renn

Keyword(s):

Field Theory ◽

Displacement Field ◽

Relativistic Theory ◽

Inertial System ◽

Field Equations ◽

Relativistic Field ◽

Relativistic Field Theory ◽

Symmetric Field ◽

Free Data ◽

General Relativistic

This chapter attempts to find a measure for the “strength” of a system of field equations, which is determined by the amount of free data consistent with the system. It introduces the infinitesimal displacement field as a necessary remedy in general relativistic theory, as one can no longer form new tensors from a given tensor by simple differentiation and that in such a theory there are much fewer invariant formations. The infinitesimal displacement field replaces the inertial system inasmuch as it makes it possible to compare vectors at infinitesimally close points. After introducing these concepts, the chapter presents a discussion on relativistic field theory.

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