Meaning of totally antisymmetric tensor

by homology
Tags: antisymmetric, meaning, tensor, totally
homology is offline
Apr1-12, 08:54 AM
homology's Avatar
P: 307
Simple question I am confused on. If I have a tensor [latex]M^{\alpha\beta\gamma}[/latex] that is totally antisymmetric in its indices then is it the case that M changes sign under the exchange of any two indices? And as a followup, a totally symmetric tensor has no sign changes on any pair exchange of indices?


Phys.Org News Partner Science news on
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
quasar987 is online now
Apr1-12, 09:09 AM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,768
What is your definition of a tensor, and of a totally antisymmetric tensor (resp. totally symmetric tensor)?
M Quack
M Quack is offline
Apr1-12, 09:16 AM
P: 637
Take a look at the Levi-Civita symbol

homology is offline
Apr1-12, 09:41 AM
homology's Avatar
P: 307

Meaning of totally antisymmetric tensor

Damn I think I figured out my problem. I was going off Carroll's definition/discussion of (anti-) symmetry (Spacetime and Geometry) which implies that an exchange of a pair of indices in a totally antisymmetric tensor yields a sign change. This is fine I realize now, what is not fine is the following.

I was looking at [latex]\partial_{\alpha}F_{\beta\gamma}[/latex]. I know that [latex]\partial_{\[\alpha}F_{\beta\gamma\]}=0[/latex] and I then INCORRECTLY assumed that [latex]\partial_{\alpha}F_{\beta\gamma}[/latex] was totally symmetric which was leading me into errors....argh....noob mistake.

Register to reply

Related Discussions
Antisymmetric connection (Torsion Tensor) Differential Geometry 6
Using cadabra to calculate antisymmetric tensor field Special & General Relativity 7
totally antisymmetric tensor Advanced Physics Homework 4
Simple identity for antisymmetric tensor Differential Geometry 4
Antisymmetric 4-tensor Special & General Relativity 3