I'm reading a book on Clifford algebra for physicists. I don't quite understand it conceptually even if I can do most algebraic manipulations. Can some-one teach me what the Clifford algebra really is? (Keep in mind that I don't know abstract algebra, nothing except some group theory.) Does it make sense to write the sum of a scalar and a bivector in the Clifford product? Both are very different things.
What's the Clifford algebra?
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0I cannot make sense of «write the sum of a scalar and a bivector in the Clifford product». – 2012-12-18
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0The Clifford product of two vectors is the sum of their inner product and the exterior product. – 2012-12-18
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0$A\wedge B+A.B =AB$ – 2012-12-18
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1The Clifford algebra is a quotient of the tensor algebra. In the tensor algebra you *can* write the sum of a vector an a scalar as a formal sum. – 2012-12-18
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1In a certain sense, the Clifford algebra is exactly what you get when you want to identify (certain) products of vectors with scalars. – 2012-12-18
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0Sorry,But what do you mean by a quotient of the tensor algebra?I have only a vague idea about what a tensor algebra is. – 2012-12-18
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0Could you please state in your question what definition of Clifford algebra you want to use? And do you know what a quotient of a mathematical structure is? – 2012-12-18
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0It might also help to say what notation you use for tensors if you want to understand the answers. – 2012-12-18
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0Well ,I have a vague idea about a quotient space in linear algebra. – 2012-12-18
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0The textbook notation is like this $ab$ is the Clifford product $A\wedge B$ is the exterior product $A\bigotimes B$ is the tensor product – 2012-12-18
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2I want to understand not in the most general case . Only the simplest. – 2012-12-18