The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [diffeomorphism-invariance]

The tag has no usage guidance.

85 questions
Filter by
Sorted by
Tagged with
42 views

Diffeomorphism invariance in special relativity

Suppose space time is the manifold $M$ isomorphic $\mathbb{R^4}$ whit the metric $-\eta_{00}=\eta_{11}=\eta_{22}=\eta_{33}=1$ in the Cartesian coordinates $\Psi(p)=(x^0,x^1,x^2,x^3)$ for $p \in M$ ....
73 views

Given the following linearized metric tensor ($c=1$) $$h_{\mu\nu}=\begin{bmatrix} 0 & f(t-z) & 0 & 0 \\ f(t-z) & 0 & 0 & -f(t-z) \\ 0 & 0 & 0 & 0 \\ ... 0answers 90 views What is a diffeomorphism invariant action made from a single vector field? Given an single vector field A_\mu(x) is it possible to make a diffeomorphism invariant action in 4 dimensions? In the same way that General Relativity is diffeomorphism invariant? My first guess ... 1answer 75 views Why don't we write the symmetric term \eta_{\mu\nu}\partial_\rho\xi^\rho in a change of coordinates in linearized gravity? Reading through this lecture, section (5.3.1): In linearized gravity, when we transform from one set of coordinates to another, the background metric remains Minkowski, but we may think of a metric ... 1answer 455 views How to show that the Einstein-Hilbert action is diffeomorphism invariant? It is often stated in texts on general relativity that the theory is diffeomorphism invariant (N.B., I am considering active diffeomorphisms), i.e. if the universe is represented by a manifold \... 3answers 846 views Why are the metric and the Levi-Civita tensor the only invariant tensors? The only numerical tensors that are invariant under some relevant symmetry group (the Euclidean group in Newtonian mechanics, the Poincare group in special relativity, and the diffeomorphism group in ... 2answers 863 views Which global symmetry of Minkowski space (if any) gets gauged to the diffeomorphism invariance of general relativity? Minkowski space has both translational and Lorentz symmetry, which together give Poincare symmetry. (It also has some discrete symmetries like parity and time-reversal that I won't be concerned with.) ... 1answer 85 views Boundary conditions due to local and global diffeomorphisms Consider the following extract from page 2 of this paper. AdS_3 is the SL(2, \mathbb{R}) group manifold and accordingly has an SL(2, \mathbb{R})_{L} \times SL(2, \mathbb{R})_{R} isometry ... 0answers 149 views Diffeomorphic manifolds of inequivalent smooth structures Given two smooth structures \mathcal A_1 and \mathcal A_2 of a spacetime manifold \mathcal M, we say that they are equivalent if \mathcal A_1 \cup \mathcal A_2 is itself a smooth structure (or ... 0answers 237 views Classical analogue of the theorem of equivalence of the S-matrix In quantum field theory there is a statement called the equivalence theorem of the S-matrix. S-matrix is invariant under reparametrization of the field. Is there in classical mechanics, the analogous ... 1answer 261 views Diffeomorphism invariance and correlation functions Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes on Quantum Gravity: In gravity, local diffeomorphisms are gauge symmetries. They are redundancies. This means ... 3answers 201 views Diffeomorphism and causality Say you have to events A and B such that A is in the future light cone of B. Now say you apply a diffeomorphism transformation x\rightarrow f(x) on the space-time, smoothly transforming the ... 2answers 563 views How do coordinate-dependent functions (not dynamical fields) transform under diffeomorphisms? Scalar fields transform under a diffeomorphism x\to\tilde x under the rule \phi(x)\to\tilde \phi (\tilde x) = \phi (x). They are often said to be invariant, though only kinda of. For example, if \... 1answer 802 views Difference between gauge invariance and diffeomorphism invariance What is the difference between gauge invariance and diffeomorphism invariance? The two seem very similar, but is the distinction between them that a gauge transformation changes the field variables ... 2answers 442 views Breaking of diffeomorphism invariance after fixing a background metric The Lagrangian for the gravitational field in absence of matter is the following$$L=1/k\int dx^4 \sqrt g R, where $k=\sqrt G$, $g$ is the determinant of the metric and $R$ the Ricci scalar. It's ...
Given a space-time coordinate of a string $X^\mu(\sigma)$ dependent on the position $\sigma$ around the string. And a string field functional $\Phi[X]$, is there a proof that the equations of motion (...