Hi Nick, i have lost.
> So, one takes actually the dotproduct op two 3-vectors, not
==========
> of 4-vectors. Let me state it otherwise : try to define the
> cross product of two 4-vectors (or a 3-vector with a 4-vector).
============
Are you talking about dotproduct or cross product?
Dot product is defined for 3 vectors and for 4 vectors.
It is natural to define it for 3*4 as dot product 3 vector * 3 vector part of 4 vector
Cross prouct is senseles for 4 vectors. And even for 3 vector it is rather
doubt. Result of cross product of two 3 vectors is not a vector at all.
It is so called pseudovector. for example magnetic field is not a vector.
If to introduce some flag in 3 vector class for pseudo vectors then
cross product will be well defined
Victor
Nick van Eijndhoven wrote:
>
> Dear friends,
> Maybe we are talking different things, but what you
> describe I understand as the dotproduct of a 3-vector D
> with the 3-vector part of a 4-vector.
> So, one takes actually the dotproduct op two 3-vectors, not
> of 4-vectors. Let me state it otherwise : try to define the
> cross product of two 4-vectors (or a 3-vector with a 4-vector).
> I would say, the cross product is only defined in 3-D space, so
> one could only take the crossproduct of a 3-vector with the 3-vector
> part of a 4-vector.
>
> Cheers,
> Nick.
>
> Victor Perevoztchikov wrote:
> >
> > "M. Sievers" wrote:
> > >
> > > On Wed, 3 Nov 1999, Nick van Eijndhoven wrote:
> > >
> > > > Hi Victor,
> > > > Maybe I am missing a point here, but the dotproduct you mention
> > > > below has to my opinion no physical meaning and as such I would
> > > > say should not be supported or at least the user should receive a
> > > > warning message that he/she is doing nonsense.
> > > > However, as I said I may be missing a point here and then I am
> > > > saying nonsense.
> > >
> > > I'd say a dot product with a three-Vector makes sense much in the same way
> > > as an angle to a three-vector does! You could make a four-vector for
> > > example by taking tracking information for the momentum and calorimeter
> > > information for the energy (should be possible...). And you should still
> > > be able to compare it to other tracks!
> > >
> > > Bye,
> > > Mike
> > Completely agree. A simple example. You have some direction (3 vector D)
> > and momentum of a track 4 vector P. Scalar production of them provide you
> > cosine of angle between them. Then this angle is used to estimate effectivity
> > etc.
> >
> > Victor
> >
> > >
> > > --------------------------------------------------------------------------
> > > Michael Sievers
> > > Michael.Sievers@desy.de
> > > --------------------------------------------------------------------------
> > > esa$ gcc -Wall -o ariane5 ariane4.c
> > > ariane4.c: 666: warning: long float implicitly truncated to unsigned type
> > > esa$ ariane5
> >
> > --
> > Victor M. Perevoztchikov perev@bnl.gov perev@vxcern.cern.ch
> > Brookhaven National Laboratory MS 510A PO Box 5000 Upton NY 11973-5000
> > tel office : 631-344-7894; fax 631-344-4206; home 631-345-2690
--
Victor M. Perevoztchikov perev@bnl.gov perev@vxcern.cern.ch
Brookhaven National Laboratory MS 510A PO Box 5000 Upton NY 11973-5000
tel office : 631-344-7894; fax 631-344-4206; home 631-345-2690
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