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Topic: What is a vector field?
Replies: 11   Last Post: Apr 30, 2013 8:57 AM

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Tom Roberts

Posts: 331
Registered: 5/8/06
Re: What is a vector field?
Posted: Apr 22, 2013 6:38 PM
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On 4/22/13 4/22/13 2:10 AM, Shmuel (Seymour J.) Metz wrote:
> In <ZPidnRFGArYb0O7MRVn_vwA@giganews.com>, on 04/20/2013
> at 09:22 PM, Tom Roberts <tjroberts137@sbcglobal.net> said:

>> Displacements from a given point form a vector space only when the
>> displacements are infinitesimal.

>
> I'm not sure what you mean by that.


Just that a set of all displacements from a given origin does not form a vector
space unless there is an isomorphism to the tangent space at the origin.


>> Hmmmm. In physics, where we always have an ORIENTABLE manifold WITH
>> METRIC,

>
> Certainly at an undergraduate level, but once you get into things like
> gauge theories you need manifolds without a metric.


Yes. I meant spacetime manifold.


Tom Roberts




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