physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, a one-loop Feynman diagram is a

connected Connected may refer to: Film and television * ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular'' * '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film * ''Connected'' (2015 TV ...

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 introduced ...

with only one cycle ( unicyclic). Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge. Diagrams with loops (in graph theory, these kinds of loops are called

cycles Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in ...

, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the '' semiclassical contributions''. One-loop diagrams are usually computed as the

integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

over one independent momentum that can "run in the cycle". The

Casimir effect In quantum field theory, the Casimir effect (or Casimir force) is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field (physics), field. The term Casim ...

Hawking radiation Hawking radiation is black-body radiation released outside a black hole's event horizon due to quantum effects according to a model developed by Stephen Hawking in 1974. The radiation was not predicted by previous models which assumed that onc ...

and

Lamb shift In physics, the Lamb shift, named after Willis Lamb, is an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which pre ...

are examples of phenomena whose existence can be implied using one-loop Feynman diagrams, especially the well-known "triangle diagram": :: The evaluation of one-loop Feynman diagrams usually leads to divergent expressions, which are either due to:Peskin, M.E. Schroeder, D.V. (1995) ''An Introduction to Quantum Field Theory.'' CRC Press. ISBN 13: 978-0-201-50397-5 * zero-mass particles in the cycle of the diagram ( infrared divergence) or * insufficient falloff of the integrand for high momenta ( ultraviolet divergence). Infrared divergences are usually dealt with by assigning the zero mass particles a small mass ''λ'', evaluating the corresponding expression and then taking the limit

\lambda \to 0

. Ultraviolet divergences are dealt with by

renormalization Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...

References

Quantum field theory Diagrams {{Quantum-stub

See also

References