Why don't we discuss the Geometric algebra and how it differs from other Clifford algebras? For introduction, here's Hestenes' home page on. Hestenes' geometric algebra and Dirac spinors are reviewed and united into a common mathematical formalism, a unification that establishes the Dirac. Yes, geometric algebra is a totally valid and accepted part of math. The proofs are correct.
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In designing a better language, one has to take decisions and make tradeoffs. Is there some feature of other clifford hestenes geometry algebra you would like to see in a better mathematical language for physics?
Physicists have sometimes invented their own math and interpretations of the math and sometimes empirically spliced two different formalisms together such hestenes geometry algebra with the use of the Pauli matrices in Quantum Mechanics. Hestene was designed as a unified mathematical language and allows one a different viewpoint on the physical interpretation of the math.
Sometimes seemingly different equations describe similar things as John Shive points out in "Similarities in Physics" or as Schrodinger showed regarding Heisenberg's Matrix Mechanics and Schrodinger's Wave Mechanics.
Geometric Algebra allows one to see some similarities more easily and get General Relativity and Quantum Mechanics speaking the same mathematical hestenes geometry algebra.
Hestenes' Geometric Algebra. What good is it? | Physics Forums
One of the problems in quantum mechanics involves complex amplitudes that has made some suggest a need for a complex probability calculus but the problem is really in interpreting what the appearance of the complex numbers mean.
For example, several physicists hestenes geometry algebra been intrigued by the idea of the Schrodinger equation as a diffusion equation with complex number elements.
Hestenes geometry algebra do Hamilton-Jacobi theory and Hamilton's optico-mechanical analogy look like in Geometric Calculus?
- Overview of Geometric Algebra in Physics
- Geometric Calculus R & D Home Page
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Thus, it supports the semantic bridge between theoretical constructs and empirical realities. Scientists make sense of hestenes geometry algebra real world by constructing models to represent the structure of things and processes within it.
Geometric Calculus provides a rich language for the construction and analysis of mathematical models.
Inferential Calculus provides a framework for their empirical validation. Hestenes, Geometry of the Dirac Theory.
Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics hestenes geometry algebra physics Kluwer: From Past to Future: Differential forms in geometric calculus. Clifford Algebras and their Applications in Mathematical Physics: Hestenes, Old Wine in New Bottles: A new algebraic framework for computational geometry.
Li, Invariant Algebras and Geometric Reasoning.
Hestenes, Wherefore a Science of Teaching?