Recent content by Jason Bennett

Hey! Can you recall which # of Susskind's lectures this was from?

This is categorically false hahaha look at oxford's theoretical physics group in the physics dept. https://www2.physics.ox.ac.uk/research/rudolf-peierls-centre-for-theoretical-physics and the and their theoretical physics group in the math dept...

Based on your comment, do you recall reading an essay of Weinberg's regarding "what a scientist should work on?" A friend of mine mentioned this essay being very good but I forgot to ask for the title! Cheers

OMG perfect thank you! :D

UGH! you're absolutely right! Thank you so much! Completely forgot that these are dummy indices (I really need to obey upper/lower even in Euclidean because I forgot about summed over indices all the time if i right things as all upper.) Cheers!

^^^ i second this question! Would love some pointers. Information theory/stat mech maybe?

I am trying to understand the following: $$ \epsilon^{mni} \epsilon^{pqj} (S^{mq}\delta^{np} - S^{nq}\delta^{mp} + S^{np}\delta^{mq} - S^{mp}\delta^{nq}) = -\epsilon^{mni} \epsilon^{pqj}S^{nq}\delta^{mp} $$ Where S^{ij} are Lorentz algebra elements in the Clifford algebra/gamma matrices...

Progress:𝜙:𝑂(3)→ℤ2𝜓:𝑂(3)→𝑆𝑂(3)𝜃:𝑂(3)/𝑆𝑂(3)→ℤ2 𝜙(𝑂)=det(𝑂) with 𝑂∈𝑂(3), that way 𝜙(𝑂)↦{−1,1}≅ℤ2, where 1 is the identity element.Ker(𝜙) = {𝑂∈𝑆𝑂(3)|𝜙(𝑂)=1}=𝑆𝑂(3), since det(𝑂)=1 for 𝑂∈𝑆𝑂(3).By the multiplicative property of the determinant function, 𝜙 = homomorphism. ***What is the form of the...

Precisely!

I am quite confused by your concern about the background topological space. Can you explain further? Please keep in mind I am very new to this area.

3) Taylor expansion question in the context of Lie algebra elements: Consider some n-dimensional Lie group whose elements depend on a set of parameters \alpha =(\alpha_1 ... \alpha_n) such that g(0) = e with e as the identity, and that had a d-dimensional representation D(\alpha)=D(g( \alpha)...

1) Likely an Einstein summation confusion. Consider Lorentz transformation's defined in the following matter: Please see image [2] below. I aim to consider the product L^0{}_0(\Lambda_1\Lambda_2). Consider the following notation L^\mu{}_\nu(\Lambda_i) = L_i{}^\mu{}_\nu. How then, does...

1) How do we determine a Lie group's global properties when the manifold that it represents is not immediately obvious? Allow me to give the definitions I am working with. A Lie group G is a differentiable manifold G which is also a group, such that the group...

Duly noted! I will do so :) Thanks

1) How do we determine a Lie group's global properties when the manifold that it represents is not immediately obvious? Allow me to give the definitions I am working with. A Lie group G is connected iff \forall g_1, g_2 \in G there exists a continuous curve connecting the two, i.e. there...