# Tag Info

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The system is a toroidal coil and we want to show that in the center of the coil (not of the torus) there is no radial component for the magnetic field. Suppose that there exists such a component in a point p. By cylindric symmetry we then know that it exists and is constant all along the circumference of the torus, at the center of the coil. Now if we ...

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Assuming no quantum gravity, $\eta^{\mu\nu}$ is a constant and can be pulled out of the derivative and what remains looks like a $\delta^k_{\mu}$ or $\delta^k_{\nu}$-type expression (in the sense of a Kronecker $\delta$), pulling the $k$ into the $\partial^\mu$ or $\partial^\nu$ respectively. If you are confused about where the minus sign comes from, I ...

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Here is my answer to some of your questions - this is based purely on my understanding of these concepts and could be wrong. (1) Whenever Lorentz transformations are a symmetry of any quantum system, they must necessarily be represented by unitary linear transformations on the quantum Hilbert space of the system. Operators representing Lorentz boosts on a ...

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Whenever you have a symmetry group $G$, it means that for each $g\in G$ there is an operator $U(g)$ (usually unitary) in the system corresponding to the action of $g$. "states behave like irrep of $G$" means that the state space can be organized into subspaces, and in each subspace $U(g)$ form an irrep of G (i.e. the matrix representation of $U(g)$).

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Let's see what relation can we find between $\alpha, \beta, \alpha^i, \beta^i$ and $\gamma, \delta, \gamma^i, \delta^i$ First using Baker Campbell Hausdorff lemma we deduce two things: $$\alpha + \beta = \gamma \text{ and } \alpha - \beta = \delta$$ because $\mathbb{1}$ commutes with $\sigma$. And e^{i\vec{\alpha}\cdot \vec{\sigma}} = \mathbb{1}\text{cos ...

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Parity and Time reversal are by definition elements of the full lorentz group with which you need to supplement the proper orthochronous subgroup in order to be able to span the entire group. As noted, the proper way to define parity in any dimension is to flip one of the spatial axes. In even space-time dimensions it so happens that flipping all spatial ...

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Hypothesis: Considering transverse stress and strain, the hexagonal unit completely tiles the space within the structure without gaps and combined with this property, comes closest to a emulating a circle which most symmetrically distributes stress and load.

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The reason behind the fact that we build our theories around perturbations of a ground state is simply that solving these equations exactly is not feasible. Hence, we try having perturbative solutions that are approximations based on supposing that the interactions are small enough that they don't deform too much the solutions to the case when there are no ...

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The consideration of ground states is an equilibrium assumption. Imagine that instead of developing a theory around a ground state we were doing it around any general state. Actually, for simplicity I'll only consider states with constant $\varphi$, but the same remarks will be valid with the appropriate modifications -- modulo some topological ...

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