Geometric Calculus

David Hestenes ()
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David Hestenes: Arizona State University, Department of Physics

Chapter Chapter 5 in Space-Time Algebra, 2015, pp 63-85 from Springer

Abstract: Abstract To complete the space-time calculus developed in chapter I, we must define the gradient operator □ for curved space-time. Evidently □ is an invariant differential operator, but we will not attempt to define it without reference to local coordinate systems. This approach simplifies comparison with tensor analysis. However, once □ is defined, manipulations can be carried out in a coordinate-independent manner. To simplify our discussion, we will ignore all questions about differentiability. Such questions can be answered in the same way as in tensor analysis. We wish to emphasize the special algebraic features of our geometric calculus.

Keywords: Gauge Transformation; Gradient Operator; Inertial System; Local Lorentz Transformation; Leibnitz Rule (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-18413-5_5

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