Questions tagged [homework-and-exercises]

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How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
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The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
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Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
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Reaction force exerted by pulley's support

Consider an in-extensible string passing over an ideal pulley connected to a block of mass $m$ as shown: The ends are pulled with a force $F$ Am I correct in saying that the block will experience a ...
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Planar Wheeled Inverted Pendulum EOM Derivation

I am building a two wheeled robot as a personal project and am having some trouble with the equations of motion. I derived a state space model but when I simulate it in scipy I get some odd behavior ...
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Solving scalar quantum field in 1+1D Milne space

So our line element is $$ds^2=dt^2-a^2t^2dx^2$$ doing following coordinate transformation y^0=t\hspace{2pt}\cosh ax, \hspace{2pt}y^1=t\hspace{2pt}\sinh ...
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Weyl transformation of Ricci tensor

We define the Weyl transform as, $$\tilde{g}_{\mu\nu}=\Omega^2g_{\mu\nu},$$ wherein $\Omega^2$ is a scalar function of space-time $x$. The Weyl transformed Christoffel symbol can be obtained by ...
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Importance of an extra total derivative term in Liouville theory

In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...
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Equilibrium points of three masses on a rigid spring ring with gravity

I'm trying to find the equilibrium points of a given system using Lagrangian mechanics (the system is still not rotating at the beginning). should I find the diagonal matrix for the characteristic ...
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Why does a salt water solution have a higher coefficient of thermal expansion (i.e. expands more) than distilled water?

I have found several different sources of data which show that a solution with a higher concentration of salt has a higher coefficient of volumetric thermal expansion than a lower concentration salt ...
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Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
In Section 7.2 of Peskin and Schroeder, the LSZ Reduction formula is discussed. I can follow the discussion leading up to the equation after (7.41) [at the bottom of Pg. 225]: \sum_\lambda \int\frac{...