# Questions tagged [approximations]

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### Why can one neglect terms quadratic in derivatives of $h_{\mu\nu}$ in linearised gravity?

In the linear approximation, terms quadratic in the Christoffel symbols are all neglected in the Riemann Tensor. However, these are not quadratic in the $h_{\mu\nu}$ but quadratic in the derivatives ...
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### 1-Loop Approximation for Fermionic Effective Action

Given a partition function $$Z = \int \mathscr{D}(\bar{\psi}, \psi) \, \mathrm{exp} \left( \, - S[\bar{\psi}, \psi] \right)$$ with fermionic (Grassmann) fields. I seek to calculate the effective ...
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### How do I derive the approximation of distance between two vectors (one being very small compared to the other)?

In solid states physics, there is an approximation that goes as follows: $$k_0|\vec{r}-\vec{R}|\approx k_0 \left(r-\frac{\vec{r}}{r} \cdot \vec{R}\right)$$ where $r$ is the norm of $\vec{r}$ and it is ...
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### Analysis of the eigenvalues of the particle in a finite square well

The eigenstates of the particle in a 1D finite square well Hamiltonian: \begin{align} H = \frac{\hat{p}^2}{2m} + V(x) \end{align} \begin{align} V(x) = \begin{cases} -V_0 & \...
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### Approximation of Rydberg Equation at Very Large $n$

I have been working the Rydberg equation with large $n$ to see how quantum systems when they become very large are functionally identical to classical systems. The problem I'm facing is trying to ...
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### Graviton fluctuation suppressed in large $N$ matters

I have a question about semiclassical gravity approximation. For probing Hawking radiation, we usually treat gravitational theory as semiclassical assuming large $N$ matters. However, I do not know ...
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### Linearized gravity: Derivatives of the metric perturbation

In linearized gravity, the metric is given by the Minkowski metric and a small perturbation, \begin{equation} g^{\mu\nu} = \eta^{\mu\nu}+h^{\mu\nu},\quad |h^{\mu\nu}|\ll 1. \end{equation} Plugging ...