Re:The Geometric Tool That Solved Einstein's Relativity Problem
by enugu on Monday August 12, 2024 @11:21PM
(#41231891)
Finite dimension tensors is interesting both in physics(ex: mechanics, electromagnetism, general relativity) and mathematics(ex: representation theory, differential geometry). Infinite dimensions is also used in physics(quantum theory) and in mathematics (Operator Algebras, representation theory again).
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Re:The Geometric Tool That Solved Einstein's Relativity Problem
by eigenket on Tuesday August 13, 2024 @07:20AM
(#41234327)
I guess? Mostly the cool applications in physics and differential geometry are about tensor fields, which are more complicated than bare tensors. You could argue that they're talking about finite dimensional tensors but tensor fields are kinda a different object (at least subjectively, to me).
Re:The Geometric Tool That Solved Einstein's Relativity Problem
by enugu on Friday August 16, 2024 @01:04AM
(#41263300)
A tensor field is a finite dimensional object varying over space. The space of all tensor fields is infinite dimensional. An operator in QM is infinite dimensional at a single point itself, and in QFT we have fields of such operators.