#LieGroups #Manifolds #Topology #Mathematics https://www.quantamagazine.org/what-are-lie-groups-20251203/

🔬🤓 Ah, the ever-mystical Lie groups—because nothing screams “fundamental to physics” like a tangled web of symbols you’ll never use outside academia! But hey, at least #Quanta offers a #newsletter so you can pretend you understand it while shopping for overpriced science merch. 🛍️📚
https://www.quantamagazine.org/what-are-lie-groups-20251203/ #LieGroups #Physics #ScienceMerch #Academia #HackerNews #ngated

Lie groups are crucial to some of the most fundamental theories in physics

https://www.quantamagazine.org/what-are-lie-groups-20251203/

#HackerNews #LieGroups #Physics #Theories #Mathematics #QuantumMechanics #FundamentalScience

#groups #RepresentationTheory #LieGroups

I've worked out that the injectivity radius under the Euclidean metric for the #unitary group U(n) is π and for real and special subgroups O(n), SO(n), and SU(n) is π√2.

This seems like a pretty basic property, but I can't find a single reference that gives the injectivity radii for any of these groups. Anyone know of one?

#DifferentialGeometry #LieGroups #Manifolds

@xameer

Cf. #DifferentialLogic • Discussion 3
• https://inquiryintoinquiry.com/2020/06/17/differential-logic-discussion-3/

#Physics once had a #FrameProblem (#Complexity of #DynamicUpdating) long before #AI did but physics learned to reduce complexity through the use of #DifferentialEquations and #GroupSymmetries (combined in #LieGroups). One of the promising features of #MinimalNegationOperators is their relationship to #DifferentialOperators. So I’ve been looking into that. Here’s a link, a bit in medias res, but what I’ve got for now.

Quantum mechanics anyone? Dozens have been disappointed by UCLA’s administration ineptly standing in the way of Dr. Mike Miller being able to offer his perennial Winter UCLA math class (Ring Theory this quarter), so a few friends and I are putting our informal math and physics group back together.

We’re mounting a study group on quantum mechanics based on Peter Woit‘s Introduction to Quantum Mechanics course from 2022. We’ll be using his textbook Quantum Theory, Groups and Representations:An Introduction (free, downloadable .pdf) and his lectures from YouTube.

Shortly, we’ll arrange a schedule and some zoom video calls to discuss the material. If you’d like to join us, send me your email or leave a comment so we can arrange meetings (likely via Zoom or similar video conferencing).

Our goal is to be informal, have some fun, but learn something along the way. The suggested mathematical background is some multi-variable calculus and linear algebra. Many of us already have some background in Lie groups, algebras, and representation theory and can hopefully provide some help for those who are interested in expanding their math and physics backgrounds.

Everyone is welcome! 

#group-theory #lie-groups #peter-woit #physics #quantum-mechanics #representation-theory

https://boffosocko.com/2023/01/26/quantum-mechanics-study-group-for-peter-woit/

I really enjoyed the paper

Oteo & Ros, Why Magnus expansion?, URL: https://doi.org/10.1080/00207160.2021.1938011 (paywall)

and not just because it cites a paper of mine (though it does help!)

It's a historical/personal reflection on the Magnus expansion, a series solution to the differential equation \( x'(t) = A(t) x(t) \) which I describe below the fold. (1/n, n≈7)

#MagnusExpansion #DifferentialEquations #MatrixExponential #QuantumMechanics #LieGroups #NumericalAnalysis #GeometricNumericalIntegration

Hi guys! Is there someone here doing research in #PDE, #LieGroups, #ComplexAnalysis?

#math #mathematics #maths