It seems that an example of such vampire particles is the photon, of which there are two types, charged photons that exist along \(t_c\) dimension but oscillates between \(t_g\) and space, and mass photon that exist along \(t_g\) and oscillates between \(t_c\) and space.
Both types of photons are in light speed in space.
Mass photon transfer energy back and forth \(t_c\) and space, effecting particles on the charge time line. When a particle receive energy along \(t_c\), it moves forward in time. When it loses the excess energy it returns. Given the random motions around the particle, it is likely to be at a different relative location when it returns. A Whacko Jump!
Charged photon transfer energy back and forth \(t_g\) and space. It would have the same effects as a mass photon but on a mass particle along \(t_g\), not on a charge.
The governing equations are the same as that from when a space dimension has been swapped for a time dimension in the wave equation. The basic wave equation applicable is,
\(\cfrac{\partial^2\psi}{\partial\,t^2_c}=ic\cfrac{\partial^2\psi}{\partial\,x\partial\,t_c}\)
and
\(\cfrac{\partial^2\psi}{\partial\,t^2_g}=ic\cfrac{\partial^2\psi}{\partial\,x\partial\,t_g}\)
where the time axis has been rotated with a space dimension. That mean this class of particles travels in space at light space.
Previously, particles of the same wave equation travels along both time axes at light speed, and can be stationary in the space dimensions but still manifest an energy, \(\psi\) around it.
Furthermore, from the post "Less Mass But No Theoretical Mass",
\(m_{\rho\,ph} c^2=m_\rho c^2-\int^{x_a}_{0}{\psi}dx=0\)
\(m_\rho c^2=\int^{x_a}_{0}{\psi}dx\)
but
\(F_{\rho\,ph}=\lim\limits_{m\rightarrow0}i\sqrt { 2{ mc^{ 2 } } }\,G.tanh\left( \cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } } (x-x_z) \right)=0\)
since photon has no mass. It is fully manifested as an energy density but does not exert a force field around it.