Appendix C. Field calculus
B. Lautrup · 2011
In continuum physics the basic mathematical objects are fields. Like the geometric objects discussed in Appendix B, fields are classified as scalar, vector, and tensor fields, each type having a different number of components. A field component is simply a real-valued function of the three spatial coordinates and time. A scalar field has only one component, a vector field has three, and a general tensor field of rank r has 3r components. In quantum physics there are also important complex fields of half-integer rank, called spinor fields, but we do not need them in classical physics.