Abstract
The properties of the unstable particles are studied by investigating the Lee model and a modified form of it. We define the unstable particle to be the complex pole of the analytically continued Green's function on the unphysical Riemann sheet. The mass and lifetime of the unstable particles are determined. Different ways of calculating the renormalization constant are discussed. The Lehmann-Symanzik-Zimmermam (LSZ) formalism is extended to include the unstable particles. Decay and scattering amplitudes for the unstable particles are calculated. The formalism is exact and does not depend on the arbitrary separation of the total Hamiltonian. Comparison with results obtained by other methods is discussed.
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