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Dmitri Pavlov
Dmitri Pavlov
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Geometric calculations using GrassmanGrassmann variables

Physicists seem to get huge computational value by introducing GrassmanGrassmann variables and GrassmanGrassmann integration into differential geometric calculations.

See: http://en.wikipedia.org/wiki/Grassmann_number

Can someone here motivate these techniques mathematically, and include the simplest pure-math example where their use and value can be illustrated. I have thought they were invented for computing volumes of constrained moduli spaces, although physicists did not originally describe them this way. Do any mathematicians use them rigorously to actually solve problems?

Geometric calculations using Grassman variables

Physicists seem to get huge computational value by introducing Grassman variables and Grassman integration into differential geometric calculations.

See: http://en.wikipedia.org/wiki/Grassmann_number

Can someone here motivate these techniques mathematically, and include the simplest pure-math example where their use and value can be illustrated. I have thought they were invented for computing volumes of constrained moduli spaces, although physicists did not originally describe them this way. Do any mathematicians use them rigorously to actually solve problems?

Geometric calculations using Grassmann variables

Physicists seem to get huge computational value by introducing Grassmann variables and Grassmann integration into differential geometric calculations.

See: http://en.wikipedia.org/wiki/Grassmann_number

Can someone here motivate these techniques mathematically, and include the simplest pure-math example where their use and value can be illustrated. I have thought they were invented for computing volumes of constrained moduli spaces, although physicists did not originally describe them this way. Do any mathematicians use them rigorously to actually solve problems?

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JoeG
JoeG
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Geometric calculations using Grassman variables

Physicists seem to get huge computational value by introducing Grassman variables and Grassman integration into differential geometric calculations.

See: http://en.wikipedia.org/wiki/Grassmann_number

Can someone here motivate these techniques mathematically, and include the simplest pure-math example where their use and value can be illustrated. I have thought they were invented for computing volumes of constrained moduli spaces, although physicists did not originally describe them this way. Do any mathematicians use them rigorously to actually solve problems?