An extension of the concept of a tensor field

[Ruslan_Sharipov]

It is known that a tensor field is a tensor-valued function T=T(p) whose argument p is a point of some space (or some manifold). However, in physics some tensor fields are produced from other tensor fields, e. g. Lagrangians in physical field theories including tensorial fields:

L=L(p,T(p),\nabla T(p)).

Exact mathematical treatement of such tensor fields with additional tensorial arguments is given in my paper

http://arxiv.org/abs/math/0503332

I invite to discuss this paper and its possible applications. One can also use this paper in order to test his/her understanding of tensors at all.

 

[Ruslan_Sharipov]

Applications to crystal physics are suggested

Applications of extended tensor fields to describing the plasticity phenomenon in crystals are suggested. See

http://uk.arXiv.org/abs/cond-mat/0504180

There is an open problem formulated as a conjecture.

 

[Ruslan_Sharipov]

An extension of the concept of spin-tensors

The concept of spin-tensors can also be extended in the same way. See the following my paper:
http://arxiv.org/abs/math.DG/0511350