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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