The mathematically exact model of (special) relativistic quantum mechanics.
Connection between information geometry and quantum mechanics.
- What is the wave equation of the particles which are moving faster than light?
- What quantities describe the particles (mass, spin, something else?) and what will be
the wave equation of the particles which live on a 1+1 and 2+1 dimensional space-time
and we consider the (special-)relativistic motion?
- Consider the 1+1 and 2+1 dimensional space-time with classical (non-relativistic, or
Galileian relativistic) symmetry.
What quantities describe the particles (mass, spin, something else?) and what will be
the wave equation of these particles?
The connection between time-travel and general relativity.
- The state space of a finite level quantum system can be endowed with
Riemannian metric using monotone metrics.
What kind of physical quantities correspond to the differential geometrycal
invariants of this space?
Noncommutative geometry and the K-theory of C*-algebras.
- If time-travelling is possible in the Gödel-universe?
- How one can make 'time-machine' using a Kerr-type rotating black-hole or a charged black-hole?
- What can we say about causality if one can travel in time?
- I have just started to study them...