# 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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### Winding number as topological invariant in Su-Schrieffer-Heeger (SSH) model

I'm studying the SSH model, here's the reference. I don't get what the definition of a topological invariant is in this case. I think the important property is that the winding number cannot be ...
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### Fundamental invariants of the electroweak sector?

In a previous question, I asked what the matrix representation of the electroweak fields is, and I was told they are identical to the Faraday tensors, but come in a set of three ($W_i, i\in \{1,2,3\}$)...
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### What does invariance of Lagrangian under a group action mean?

Let $L(q_i,\dot{q_i},t)$ be the(a?) Lagrangian of a physical system. Assume that the gen. coordinates $q_i$ transform under a certain Group G as $q_i\rightarrow q_i'=f_i(q_j,\theta_k)$ where $f_i$ are ...
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### Transformation of Lagrangian and action

Consider the Lagrangian $L(q_i,\dot{q_i},t)$ for $i=1,2, ...n$. Transform (invertibly) $q_i$ to another set of generalized coordinates $s_i=s_i(q_j,t)$. Now, in a different scenario, consider ...
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### Is metric in GR invariant?

In SR, the central theme is the invariance of Lorentz metric, but under a particular Lorentz transformation. In GR, a metric is a solution to the Einstein’s field equation and there can be all kinds ...
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### Show invariance of the inner product of $4$-velocities in different frames

In the lab frame, particle $B$ moves to the right with speed $u$, and particle $C$ moves to the left with speed $v$. In the frame of $C$, particle $B$ is seen to move to the right with speed $w$, ...
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I am studying the conformal group in 3 dimensions. The generators of this group are isomorphic to the generators of $SO(1,4)$. Hence two of the Casimir operators are, $$C_1=-\tfrac12J_{AB}J^{AB}$$ $$... 0answers 73 views ### Reparametrization of einbein action I would like to show that the following action$$ \mathcal{S}=-\frac{1}{2}\int{d\tau \sqrt{-g_{\tau\tau}}\left(g^{\tau\tau}\eta_{\mu\nu}\frac{dx^\mu}{d\tau}\frac{dx^\nu}{d\tau}+m^2\right)} $$is ... 2answers 42 views ### Invariant Interval Interpretation Thanks for reading. The invariant interval between two events is defined as... S^2=(ct)^2-(x)^2 ...where t is the time between the events and x is the distance between the events. When its ... 1answer 138 views ### Lorentz Invariance of the Euler-Lagrange equation for fields Given an Lorentz invariant Lagrangian density L of a Lorentz invariant scalar field \phi, How does one show that the following term in the Euler-Lagrange equation is invariant under Lorentz ... 0answers 31 views ### Charge is relativistic invariant. What does it mean? [duplicate] Yesterday my teacher stated this statement that charge is relativistic invariant But he didn't explained this statement. So can anyone explain me this statement? 2answers 74 views ### Casimir operators for Poincare algebra I have seen at various places the comment that the operator P_\mu P^\mu is a Casimir operator of Lorentz algebra and thus it satisfies a on-shell condition like P_\mu P^\mu=m^2. Given the Poincare ... 1answer 69 views ### Variables of an SO(3)-invariant function (hamiltonian) I am looking to reduce the dependence of a function, knowing that it satisfies some invariance constraints. Let me first formulate my question by explaining the 2-dimensional case. Imagine I have a ... 0answers 69 views ### Why does invariance commute with partial derivative? This question applies more generally to actions, but I am going to ask it for a specific example. I am getting confused when considering the invariance of the superstring action under Weyl ... 5answers 2k views ### Why can't the constancy of the speed of light be deduced from classical physics? [closed] I have read over a dozen questions about the speed of light -- "why it c constant?", "why can't anything travel faster than light?", "how do we know this?" The responses are quite clear: The ... 3answers 609 views ### Why Pauli matrices are the same in any frame? [duplicate] On page 157 of Schwartz's QFT book, He write that “\sigma_i do not change under rotations”. If so, changes in \psi and B cancels, so we can get that (\vec{\sigma} \cdot \vec B)\psi is ... 2answers 228 views ### How to show that scalar fields are translation invariant? Classical scalar fields governed by Klein-Gordon equation,$$\left(-\frac{\partial^2}{\partial t^2}+\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}+m^2\...
I'm trying to follow the answer to this post, that cites the identity $$\epsilon_{i_{1} \ldots i_{n}} A_{j_{1}}^{i_{1}} \cdots A_{j_{n}}^{i_{n}}=\operatorname{det} A \epsilon_{j_{1} \ldots j_{n}}$$...
### What is the problem with a generalized kinetic term as $K^{\mu\nu}(x)\partial_\mu\phi\partial_\nu\phi$?
For field theory in flat spacetime, the most general kinetic term that I can think of for a field is $$K^{\mu\nu}(x)\partial_\mu\phi\partial_\nu\phi$$ where $K^{\mu\nu}(x)$ is an arbitrary second rank ...