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In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. [ 1 ] [ 2 ] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert , the Simon problems concern quantum operators . [ 3 ]
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use ...
Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU( n ) , or more generally any compact Lie group .
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics.
A well understood and illustrative example of an instanton and its interpretation can be found in the context of a QFT with a non-abelian gauge group, [note 2] a Yang–Mills theory. For a Yang–Mills theory these inequivalent sectors can be (in an appropriate gauge) classified by the third homotopy group of SU(2) (whose group manifold is the ...
Caron-Huot does research on scattering amplitudes in quantum chromodynamics and N=4 supersymmetric Yang-Mills theory, as well as the quark-gluon plasma in heavy ion collisions. [7] He, with colleagues such as Nima Arkani-Hamed , Freddy Cachazo , and Johannes Henn, have done research on symmetries that link gravity, the energy levels of the ...
Simon's problem considers access to a function : {,} {,}, as implemented by a black box or an oracle. This function is promised to be either a one-to-one function, or a two-to-one function; if is two-to-one, it is furthermore promised that two inputs and ′ evaluate to the same value if and only if and ′ differ in a fixed set of bits. I.e.,
In mathematics, and in particular gauge theory and complex geometry, a Hermitian Yang–Mills connection (or Hermite–Einstein connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue of Einstein's equations: namely, the contraction of the curvature 2-form of the connection with the Kähler form is ...