If a pseudovector is explicitly given by a cross product of two vectors ( as opposed to entering the cross product with another vector ), then such pseudovectors can also be written as antisymmetric tensors of second order, with each entry a component of the cross product.
22.
An even simpler variant of this model is to let M here be a numerical antisymmetric tensor, in which context it is usually denoted \ theta, so the relations are [ x _ \ mu, x _ \ nu ] = i \ theta _ { \ mu \ nu }.
23.
There is another vector quantity not often discussed it is the time-varying moment of mass ( " not " the moment of inertia ) related to the boost of the centre of mass of the system, and this combines with the classical angular momentum to form an antisymmetric tensor of second order.
24.
Are reducible, which means they can be re-expressed in terms of "'a "'and "'b "'as a rank 0 tensor ( scalar ), plus a rank 1 tensor ( an antisymmetric tensor ), plus a rank 2 tensor ( a symmetric tensor with zero trace ):
25.
As an important example of this, 11D-Supergravity contains a 3-form antisymmetric tensor with a 4-form field strength, and consequently prefers to compactify 7 or 4 of its space-like dimensions, so the large-scale spacetime must be either 4 or 7 dimensional, the former of which is attractive from a phenomenological perspective
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