Mass operator
operator of mass
The operator taking account of the interaction of a particle with its own field and other fields. Let the state of a system be described by the quantity
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where is the field operator acting on the wave function
(the state vector) and
is a four-dimensional coordinate vector. If
satisfies the equation
![]() | (*) |
where the operator corresponds to a free particle and
accounts for its interaction with the particle's own field and other fields, then
is called the mass operator. The mass operator is an integral operator with kernel
:
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The mass operator is closely related to the one-particle Green function , which is a solution of an equation similar to (*) but with a
-function source on the right-hand side:
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where is the four-dimensional delta-function.
References
[1] | N.N. Bogolyubov, D.V. Shirkov, "Introduction to the theory of quantized fields" , Interscience (1959) (Translated from Russian) |
[2] | A.A. Abrikosov, L.P. Gor'kov, I.E. Dzyaloshinskii, "Methods of quantum field theory in statistical physics" , Prentice-Hall (1963) (Translated from Russian) |
Comments
The concept of a "mass operator" can only be given some sense in the context of quantum field perturbation theory, and plays a minor role in that context.
Mass operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mass_operator&oldid=47782