# Questions tagged [invariants]

This tag is for questions relating to invariant, a property of a system which remains unchanged under some transformation. In physics, invariance is related to conservation laws.

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### The confusion over the invariance of the correlation function and the mutually local field in the CFT

Consider the correlation function $$\langle \Pi_{i=1}^n V_i(z_i,\bar z_i) \rangle$$ such as $$\langle V_1(z_1) V_2(z_2) \rangle,(z_1>z_2)$$ by position the $z_i$ correctly, the exchange of the ...
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### How do you prove $d\tau = dt/\gamma$ is a Lorentz invariant? [closed]

How do you prove $d\tau = dt/\gamma$ is a Lorentz invariant?
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### Spin as Poincaré invariant label

I was thinking about how we construct unitary representations for the Poincaré group in the case of massive particles. We move to a frame where the particle is at rest, and here the little group that ...
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### Help me understand the CPT signatures of different physical quantities

I am an engineer and not a trained physicist, but still I am fascinated by symmetries and I want to understand them. Specifically, in a paper ¹ I found the below table which covers a large number of ...
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### Is physical energy is invariant under reflection?

I am wondering whether the energy landscape of a physical system (in particular a molecular conformation) can be considered invariant under reflection of the 3D space. My understanding is that some ...
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### Invariant lagrangian under $SU(N)$

I know from group theory that $\bar{R} \otimes R \otimes A= 1 \oplus \dots$ where $A$ is the adjoint representation. My question is how to build the singlet, I thought a generalization of Rodriguez's ...
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### Are one-dimensional tensors of arbitrary rank just scalars?

Consider a tensor of arbitrary rank (2 for this case) $A_{ij}$, and dimension one. Granted there are two indices to specify a component, but since each index can only take one value, there is only one ...
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### Reaction-Threshold Energy

I have this exercise: "Given the following reaction : $K^+ + n \rightarrow \pi^+ + \Lambda$ find : threshold energy of $K^+$, $E_{Kmin}$, to make the reaction happen. $E_{K^+}$ and $P_{\pi^+}$...
Consider the following decay : $$K^+\longrightarrow \pi^0 + e^+ + l^0$$ where $l^0$ is a neutral lepton. What kind of particle is $l^0$? For $K^+$ , if it's at rest, ...