(a) particles which can not be observed are called virtual particles A 4-vector momemtum is p = (p,i E) so that
(4 − momentum)2 = (3 momentum Space )2 − (energy)2 time
The components p1,2,3 are said to be spacelike and the energy component E, timelike. If q denotes the 4-momentum transfer in a reaction i.e. q = p−p , where p, p are initial and 4-momenta, then
q2 > 0 is spacelike as in the scattering process
q2 < 0 is timelike as for (mass)2 of free particle
q2 = 0 is lightlike
(b) The relativistic relationship between total energy, momentum and mass for the field quantum is
E2 − p2 c2 − m2 c4 = 0 (1)
We can now use the quantum mechanical operators
To transform (1) into an operator equation
representing the force between nucleons by a potential ϕ(r, t) which may be regarded as a field variable, we can write
as the wave equation describes the propagation of spinless particles in free space. The time independent part of the equation is
For m = 0, this equation is the same as that obeyed in electromagnetism, for a point charge at the origin, the appropriate solution being
where ε0 is the permittivity.
