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scottbekerham
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Is geometric algebra and geometric calculus worth learning for a theoretical physicist? What are the advantages of this approach against the usual vector calculus ?
scottbekerham said:So why isn't it mainstream? Is it because it's new or what? Shouldn't it replace ordinary vector calculus if it's easier to work with and provide geometrical approach far superior than ordinary calculus?
Geometrical algebra in theoretical physics is a mathematical framework that combines the concepts of traditional vector algebra, linear algebra, and differential geometry. It is used to describe physical phenomena in a more geometrically intuitive and elegant way.
Traditional vector algebra only deals with quantities that have magnitude and direction, whereas geometrical algebra also incorporates the concept of orientation. This allows for a more comprehensive understanding of physical systems and their behavior.
Geometrical algebra allows for the representation of complex physical systems in a more compact and intuitive manner. It also allows for the formulation of equations that are independent of a specific coordinate system, making it easier to generalize and apply to different situations.
Yes, geometrical algebra has been successfully applied in various fields of theoretical physics such as classical mechanics, electromagnetism, quantum mechanics, and general relativity. It provides a unified framework for understanding these different areas of physics.
It can be challenging to learn geometrical algebra initially, especially for those who are not familiar with vector calculus and differential geometry. However, with practice and patience, it can be a powerful tool for solving complex problems in theoretical physics.