Recent content by snypehype46

To calculate the Riemann coefficient for a metric ##g##, one can employ the second Cartan's structure equation: $$\frac{1}{2} \Omega_{ab} (\theta^a \wedge \theta^b) = -\frac{1}{4} R_{ijkl} (dx^i \wedge dx^j)(dx^k \wedge dx^l)$$ and using the tetrad formalism to compute the coefficients of the...

Ok I see, so for the term ##\Gamma^3_{[13]}##, we used the last equation. My point of confusion is why we don't care about the factor involving ##\theta^2 \wedge \theta^3##

@martinbn what is the meaning of the dots?

I'm reading "Differentiable manifolds: A Theoretical Physics Approach" by Castillo and on page 170 of the book a calculation of the Ricci tensor coefficients for a metric is illustrated. In the book the starting point for this method is the equation given by: $$d\theta^i = \Gamma^i_{[jk]}...

I'm learning string theory from the book by Zwiebach and others. I'm trying to understand the quantisation of the open string and its mass spectrum. In light-cone gauge the mass-shell condition of an open string is given by: $$M^2 = 2(N - 1)/l_s^2$$ where ##N =...

I'm trying to the following exercise: I've proven the first part and now I'm trying to do the same thing for fermions. The formulas for the mode expansions are: What I did was the following: $$\begin{align*} \sum_s \int d\tilde{q} \left(a_s(q) u(q,s) e^{-iq \cdot x}+ b_s^\dagger(q) v(q,s)...

I have the following lagrangian density: $$L = \bar{\psi}i \gamma^\mu \partial_\mu \psi - g\bar{\psi}(\sigma + i\gamma^5\pi)\psi + \frac{1}{2}(\partial_\mu \sigma)^2+ \frac{1}{2}(\partial_\mu \pi)^2 -V(\sigma^2 + \pi^2)$$ where $\pi$ and $\sigma$ are scalar fields. I have show that this...

This is not really homework assigned to me but I wasn't sure where to post this. I'm trying to work through the book "Quantum Field Theory for Gifted Amateurs" by Tom Lancaster. I'm doing the questions on Chapter 19 to understand how to draw Feynman diagrams and work out their amplitude. One of...

Thanks for the reply. Yes, I think I understand that is what's intended. My question is more: why is it not possible to find such a functor?

I have a question that is related to categories and physics. I was reading this paper by John Baez in which he describes a TQFT as a functor from the category nCob (n-dimensional cobordisms) to Vector spaces. https://arxiv.org/pdf/quant-ph/0404040.pdf. At the beginning of the paper @john baez...