Are the intermediate vector bosons real (like the electrons) or just mathetical constructs?i have got a theory to unify the 4 forces, but it does not tell anything about exchange particles in case of the weak force.I could proceed only if they are imaginary.
I see that you are of the age of a highschool student, as I could be your grandma please do not take offense in the tone of my answer.
Are the intermediate vector bosons real (like the electrons) or just mathetical constructs?
The W and the Z are real particles measured in the lab, as real as the electrons and photons.
In the title you ask:
Exchange particles-real or just mathematical constructs?
Exchange particles are mathematical constructs in the Feynman diagrams used to calculate branching ratios and cross sections for real interactions. The exchanged particles are virtual because although they have all the quantum numbers characterizing their name, their four momentum vector is off mass shell. All particles can be virtual within the Feynman diagrams, which are a valuable method of simplifying the writing of unique integrals for the reactions. The electrons too can be virtual in more complicated interactions.
The intermediate particles are virtual in all four diagrams, the end particles are real.
The basic concept is that the forces we observe experimentally between two particles are due to the exchange of virtual particles .
We know of four forces:
the electromagnetic with the photon being the mediator. the weak with the Z and W bosons being the mediators the strong with the gluon being the mediator the gravitational with the graviton ( this is hypothetical) ""
i have got a theory to unify the 4 forces, but it does not tell anything about exchange particles in case of the weak force.I could proceed only if they are imaginary.
The problem with a unified theory of all four forces is not of postulating a unification. It is of embedding in the theory the Standard Model. The SM encapsulates very many data collected with experiments the last 100 years in a mathematically elegant way and has to be part of any unification mathematical construct.
At the moment string theories are well on the way of getting a quantized unified theory of all four forces .
I think it would be best for you to start studying the existing frameworks instead of spending effort in mathematical constructs that most probably would not fit the plethora of all the known experimental data.
Not only are electrons not vector bosons, as innisfree said, but the actual vector bosons ($W^\pm,Z$) are definitely real. Or at least no less real than any other particles which had well defined experimental signatures predicted which were then confirmed when people built the appropriate experiments. Depending on how philosophical you want to get we only ever deal with mathematical abstractions in physics, and never with what is really real, whatever that is supposed to mean. The situation is no different for the vector bosons than for any other particle in the standard model. If your theory can't reproduce all of the phenomenology explained by the vector bosons then it is ruled out at a very high confidence.
The vector bosons are most definitely real, albeit short-lived particles.
The "exchange" particles that you see in the interior of Feynman diagrams are NOT real, observable states, but are mathematical conveniences that make doing perturbation theory easier.
So, the question is what you're asking about.