Eva Miranda

speaker

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

And you are a good student.

What are the coefficients of the vector field?

These are the Hamilton's equations.

So Hamilton's equations are just the equations of the trajectories of the vector field.

If I if I compute this vector field, I'm going to get a vector field whose first component is partial of H with respect to P, and the second minus partial of H with respect to Q.

Okay.

So indeed what happens is that this equation that we write here gives us a vector field that is just a vector field whose uh if I compute the trajectories of this vector field, I get Hamilton's equation.

Can I say that these two form controls classical mechanics, these two forms?

Yes I can.

Okay, so I'm going to give a name to this form.

This this is a geometrical structure and it's called a symplectic form.

So here I took a particular example of symplectic form, which is this one in this form.

I can always locally think that he's of this sort form, thanks to Darbu, who is not the guy in this picture.

And

I'm talking about symbolic structures and why do we need now another geometrical structures?

Because we have always been talking about Riemannian geometry, right?

Riemannian geometry is important.

also generalizations of Riemannian geometry are important to to relativity, so why do we need now another geometry?

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