Eva Miranda

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1,609 appearances 1 recordings 1 series first heard Jan 2025 last heard Jan 2025

Eva Miranda’s voice in public audio — every appearance, attributed to the second.

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Theories of Everything with Curt Jaimungal · Eva Miranda: The Mathematical Bridge Between Classical and Quantum · 26 Jan 2025 podcast

I take a basis of this Li algebra, which is the Li algebra of SO3.

So it's the Li algebra of the space of all possible rotations in three dimensions.

Okay?

And now I compute these brackets.

Okay, I did it for you.

They are not zero, they give me precisely the other vector.

Okay.

Now I can define a Poisson bracket.

Doing something that looks very strange, which is to take the dual basis of these vectors.

And this gives me some Poisson brackets.

Okay.

To have a Poisson bracket.

I need uh some conditions.

I need to have skew symmetry, anti-symmetry, and I need to have that this uh Jacobi identity is satisfied, which is something that is satisfied for the commutator of matrices.

And and you know what?

This uh Poisson bracket cannot be the Poisson bracket of a symplectic manifold.

Do you uh do you see why?

Yeah.

What uh what you are doing when you are doing the algebras.

You can m uh visualize these uh kind of uh products.

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