Science > Physics > Can a three dimensional shape have negative parity?
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Science > Physics |
| User: |
"" |
| Date: |
14 Jul 2007 05:45:07 AM |
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Can a three dimensional shape have negative parity? |
This question is to straighten out my ideas. In physics,
positive parity
means that a shape is invariant under reflection, such as
a sphere. There are many other examples.
When does a shape have NEGATIVE parity? Or can a
shape (say a glove) have negative parity at all?
Or phrased in another way: are there 3-d shapes
(or 3d objects) that represent pseudoscalars or
pseudovectors (which both have negative parity)?
Regards
Frank
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| User: "Igor" |
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| Title: Re: Can a three dimensional shape have negative parity? |
14 Jul 2007 12:38:05 PM |
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On Jul 14, 6:45 am, wrote:
This question is to straighten out my ideas. In physics,
positive parity
means that a shape is invariant under reflection, such as
a sphere. There are many other examples.
When does a shape have NEGATIVE parity? Or can a
shape (say a glove) have negative parity at all?
Or phrased in another way: are there 3-d shapes
(or 3d objects) that represent pseudoscalars or
pseudovectors (which both have negative parity)?
Regards
Frank
Three dimensional volumes will always have negative (odd) parity,
since they are essentially pseudo-scalars. Think of the classical
parallelopiped where the volume is defined as A dot (B cross C), where
(A,B,C) are the vectors that define the three independent edges. This
is indeed a pseudo-scalar since it will invert under reflections.
Two dimensional area, on the other hand, will always have positive
(even) parity, since the area of a parallelogram can be represented as
the cross product of two vectors, which is invariant under
reflections.
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| User: "" |
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| Title: Re: Can a three dimensional shape have negative parity? |
15 Jul 2007 01:54:01 AM |
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On 14 Jul., 19:38, Igor <thoov...@excite.com> wrote:
Three dimensional volumes will always have negative (odd) parity,
since they are essentially pseudo-scalars. Think of the classical
parallelopiped where the volume is defined as A dot (B cross C), where
(A,B,C) are the vectors that define the three independent edges. This
is indeed a pseudo-scalar since it will invert under reflections.
Two dimensional area, on the other hand, will always have positive
(even) parity, since the area of a parallelogram can be represented as
the cross product of two vectors, which is invariant under
reflections.
Ok, my question was about 3 dimensions. If all shapes in 3d have
negative parity almost naturally, what would a shape with POSITIVE
parity look like? Is such a shape possible at all?
From your email it seems that even an infinitely long tube would have
negative parity. Is there any other option to get positive parity?
Frank
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