In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
, a tadpole is a one-loop
Feynman diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introdu ...
with one external leg, giving a contribution to a one-point
correlation function
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables re ...
(i.e., the field's
vacuum expectation value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. ...
). One-loop diagrams with a
propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. ...
that connects back to its originating vertex are often also referred as tadpoles. For many massless theories, these graphs vanish in
dimensional regularization
__NOTOC__
In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Fey ...
(by
dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as ...
and the absence of any inherent
mass scale in the
loop integral
In quantum field theory and statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. These integrals are used to determine counterte ...
).
Tadpole corrections are needed if the corresponding external field has a non-zero vacuum expectation value, such as the
Higgs field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field,
one of the fields in particle physics theory. In the Standa ...
.
Tadpole diagrams were first used in the 1960s. An early example was published by
Abdus Salam
Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Punjabi Pakistani theoretical physicist and a N ...
in 1961, though he did not take credit for the name.
Physicists
Sidney Coleman
Sidney Richard Coleman (7 March 1937 – 18 November 2007) was an American theoretical physicist noted for his research in high-energy theoretical physics.
Life and work
Sidney Coleman grew up on the Far North Side of Chicago. In 1957, h ...
and
Sheldon Glashow
Sheldon Lee Glashow (, ; born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, Emeritus, at Harvard ...
made an influential use of tadpole diagrams to explain symmetry breaking in the strong interaction in 1964.
In 1985 Coleman stated (perhaps as a joke) that Physical Review’s editors rejected the originally proposed name "spermion".
References
Quantum field theory
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