In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
, the Scherk–Schwarz mechanism (named after
Joël Scherk
Joël Scherk (; 27 May 1946 – 16 May 1980) was a French theoretical physicist who studied string theory and supergravity.
Work
Scherk studied in Paris at the École Normale Supérieure (ENS). In 1969 he received his diploma (Thèse de troisiè ...
and
John Henry Schwarz
John Henry Schwarz ( ; born November 22, 1941) is an American theoretical physicist. Along with Yoichiro Nambu, Holger Bech Nielsen, Joël Scherk, Gabriele Veneziano, Michael Green, and Leonard Susskind, he is regarded as one of the founders ...
) for a field φ basically means that φ is a
section
Section, Sectioning, or Sectioned may refer to:
Arts, entertainment and media
* Section (music), a complete, but not independent, musical idea
* Section (typography), a subdivision, especially of a chapter, in books and documents
** Section sig ...
of a non-
trivializable fiber bundle
In mathematics, and particularly topology, a fiber bundle ( ''Commonwealth English'': fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space E and a pr ...
(not necessarily a
vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to eve ...
since φ needn't be linear) which is fixed by the model. This is called a ''twist'' by physicists.
Note that this can never occur in a
spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
which is
homeomorphic
In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function betw ...
to R
n, which is a
contractible space
In mathematics, a topological space ''X'' is contractible if the identity map on ''X'' is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is one that can be continuously shrunk to a point within t ...
.
However, for
Kaluza–Klein theories, the Scherk–Schwarz mechanism is a possibility which can't be neglected.
Particle physics
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