Particles with complex number mass.

[MathematicalPhysicist]

I was thinking in the bus, we have theoretically speaking particles such as tachyons with imaginary number for their mass. These particles if they exist always run at speeds higher than c.

My question is has anyone thought of modifying perhaps Lorentz transformations to give us the possiblity of a complex number mass' particles.

Well, you might ask what does the imaginary part of the mass will signify, well this is really a physical interpretation I rather not go here yet.

 

[maajdl]

The Lorentz transformation does not involve any particle.
It deals with the transformation of coordinates.
Of course it can be applied to the coordinates of some particle, but the properties of the particles play no role, only the coordinates matter.

 

[Fedecart]

Well, actually in any quantum field theory the particles are represented by states in a fock space, and there is a different specie of particle for any infinitedimensional representation of the Poincarè group...
In fact, Lorentz transformations do fix which kind of particles are allowed.
If the invariance group of the theory would be something other than $SO(1,3)$ then other particles would be preticted.

 

[Demystifier]

The relevant quantity is not the mass, but the mass squared. It is a real quantity for both ordinary and tachyon particles, which is why they make sense. Complex mass would correspond to mass squared which is not a real quantity, so it would not make sense physically. At least not in classical physics.

In quantum physics it might make sense because complex mass (and mass squared) would be a property of the wave function, which, of course, does not need to be real.

 

[MathematicalPhysicist]

The relevant quantity is not the mass, but the mass squared. It is a real quantity for both ordinary and tachyon particles, which is why they make sense. Complex mass would correspond to mass squared which is not a real quantity, so it would not make sense physically. At least not in classical physics.

In quantum physics it might make sense because complex mass (and mass squared) would be a property of the wave function, which, of course, does not need to be real.

Well, you can take its $$mm^* = |m|^2$$ to make sense of it.