The Heisenberg, interaction, and Schrödinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are polynomial or convergent power series in field operators and their first derivatives. The general links between different time-dependent pictures of motion ar...

A 2-knot will be a 2-sphere embedded into R locally flatly. Although we cannot see a 2-knot directly with our eyes, there are several ways to visualize it. A motion picture is one of the ways. Roughly speaking, a motion picture is a CT scan (Computed Tomographic scan) of a 2-knot. It is a one-parameter family of slices of a 2-knot, that are 0or 1-dimensional objects in R. The n-twist-spun trefo...