Supermathematics is the branch of
mathematical physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...
which applies the mathematics of
Lie superalgebra
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a \Z/2\Z grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry.
The notion of \Z/2\Z gra ...
s to the
behaviour
Behavior (American English) or behaviour (British English) is the range of actions of Individual, individuals, organisms, systems or Artificial intelligence, artificial entities in some environment. These systems can include other systems or or ...
of
bosons
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-integer ...
and
fermions
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and ...
. The driving force in its formation in the 1960s and 1970s was
Felix Berezin.
Objects of study include
superalgebra
In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.
T ...
s (such as
super Minkowski space
In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base manifold (or rather, supermanifold) for superfields. It is acted on by the super Poincaré a ...
and
super-Poincaré algebra
In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal sym ...
),
superschemes,
supermetric Supermetric is a mathematical concept used in a number of fields in physics.
See also
* Supergeometry
*Supergravity
* Super Minkowski space
*Gauge gravitation theory
In quantum field theory, gauge gravitation theory is the effort to extend Yang– ...
s/
supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
,
supermanifold
In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below.
Informal definition
An informal definition is com ...
s,
supergeometry
Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field the ...
, and
supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
, namely in the context of
superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
'Superstring theory' is a shorthand for supersymmetric string t ...
.
References
"The importance of Lie algebras" Professor
Isaiah Kantor,
Lund University
Lund University () is a Public university, public research university in Sweden and one of Northern Europe's oldest universities. The university is located in the city of Lund in the Swedish province of Scania. The university was officially foun ...
External links
*
Felix Berezin, The Life and Death of the Mastermind of Supermathematics', edited by
Mikhail Shifman
Mikhail "Misha" Arkadyevich Shifman (; born 4 April 1949) is a theoretical physicist (high energy physics), formerly at the Institute for Theoretical and Experimental Physics, Moscow, Ida Cohen Fine Professor of Theoretical Physics, William I. ...
, World Scientific, Singapore, 2007,
Mathematical physics
Supersymmetry
Lie algebras
String theory
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