# Questions tagged [covariance]

How a quantity behaves under a change of basis vectors. This tag covers relativistic covariance, as well as contravariant and covariant tensors not necessarily in the context of relativity. DO NOT USE THIS TAG for statistical covariance.

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### Derivatives in Poincare' gauge theory

I have been reading the lectures: http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartIII_Supergravity.pdf about Poincare' gauge theory. The Poincare' group is considered as semidirect ...
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### Why aren't Christoffel symbols tensors? - asked from a fibre bundle perspective

I've been reading about connections on fibre bundles recently and it's made me think about the exact nature of the Christoffel symbols in GR. If we have a vector bundle $E$ over $M$ and put a ...
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### Gamma matrices in curved spacetime

How to raise and lower indices of gamma matrix in curved spacetime? Do we raise and lower the index of gamma matrix with $g_{\mu \nu}$?
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### covariant and contravariant form of a matrix

I'm following a paper to solve this equation: $y_{j}=y_{o}$ + A$\eta^{T}$ (Eq. 2) My question is about the term $\eta^{T}$. In the paper says: "With symbol $\eta$, we denoted a 1 × 6 ...
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### Covariant version of the Coulomb gauge

In curved spacetime, it is possible to define the covariant version of the Lorenz gauge, going from $\partial_\mu A^\mu =0$ to $\nabla _\mu A^\mu =0$ in some curved spacetime $g_{\mu \nu}$. What is ...
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### General Covariance, what does Einstein mean?

I have read the papers by Einstein and I am convinced I understand what he means completely. Given there are controversies, maybe I over understood it: It is I am convinced, can be said in two ...
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### Is there any example of a physical theory which isn't invariant under translations?

Isn't it trivial that all physical theories in spacetime are invariant under local translations? Is there an example of a theory which isn't invariant under translations? Please, take note that I'm ...
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### Showing that the angular momentum transforms as a vector

I define a vector as any object $(a_i,a_j, a_k)$ such that it transforms the same way as the coordinates themselves. That is if $x'_i = R_{ij}x_j$, then $a'_i = R_{ij}a_j$. Please correct me if this ...
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### Showing path integral formalism is Lorentz-invariant without resorting to Hamiltonian formalism

I think people typically say that path integral formalism is manifestly Lorentz-invariant, because Lagrangian density is Lorentz-invariant. However, path formalism is typically defined with time ...
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### Covariant Formulation of E&M

Can anybody explain me what does mean the "covariant formulation of electrodynamics"? What does the covariant here mean? Invariance of Maxwell equations under Lorentz Transformations? In what way? ...
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### How does effective potential transform under coordinate transformation?

Let us say we have an equation of motion of the following form, $$\ddot{x}=g\tag{1}$$ For this system an effective potential can be defined as, $$\ddot{x}=-\dfrac{d}{dx}U_\text{eff}$$ U_\text{...
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### Can an equation containing a specific tensor be Lorentz invariant?

Let $A_u$ be a vector field in spacetime. If we restrict to a $2+1$ spacetime, and define the Levi-Civita tensor $\epsilon^{uvp}$ by $\epsilon^{123}=1$, then is the following equation Lorentz ...
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### A fundamental question about tensors and vectors [closed]

Studying relativity, I am deeply confused with the fundamental concept of vectors and tensors. Are they some specific "realities" that "exist" independently of coordinates? If so, given a vector \$\...
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### Action in curved space

I am reading Carroll's book on GR and am confused about the generalization of the action principle to curved space. Please refer to the snippet from the book below. After writing equation 4.47, we ...
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### What is invariance of an equation?

I'm confused. Suppose we have a Schrodinger equation with a time-independent Hamiltonian: \begin{align} i\frac{\partial}{\partial t}\psi(x, t) = H\psi(x, t). \tag{1} \end{align} Under time reversal ...