scalar product and isospace


by parton
Tags: isospace, product, scalar
parton
parton is offline
#1
Mar2-09, 03:52 PM
P: 84
In some textbooks you can find that a term
[tex] \vec{\tau} \cdot \vec{A}_{\mu} = \sum_{a=1}^{3} \tau_{a} \, A_{\mu}^{a} [/tex]
is called scalar product in isospace (where the tau's denotes the Pauli matrices and [tex]A_{\mu}^{a}[/tex] is a four-vector). But how can one call this "scalar" product. The product is a matrix and not a scalar. And the usual definition of a scalar product requires that the product has to be a scalar.

Or take another example: [tex] \gamma^{\mu} \, A_{\mu} [/tex] is called a scalar product of four-vectors in space-time. It is confusing. Could anyone explain that to me? Do we really have a scalar product (in a strict mathematical sense) or is it just a convention done by physicists?
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)

Register to reply

Related Discussions
second Hermitian scalar product Calculus & Beyond Homework 0
Scalar Product of a diffrential. Calculus 1
The scalar product Precalculus Mathematics Homework 1
scalar product question Introductory Physics Homework 12