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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. A Yang–Mills theory seeks to describe the ...
The Yang–Mills equations are gauge invariant. Mathematically, a gauge transformation is an automorphism of the principal bundle , and since the inner product on is invariant, the Yang–Mills functional satisfies. and so if satisfies (1), so does . There is a moduli space of Yang–Mills connections modulo gauge transformations.
[2] [4] This result includes the following special cases: All non-flat Yang–Mills connections with positive sign over S n {\displaystyle S^{n}} with n > 4 {\displaystyle n>4} are unstable. [ 6 ] [ 7 ] [ 8 ] James Simons presented this result without written publication during a symposium on "Minimal Submanifolds and Geodesics" in Tokyo in ...
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N = 4 super Yang–Mills can be derived from a simpler 10-dimensional theory, and yet supergravity and M-theory exist in 11 dimensions. The connection is that if the gauge group U( N ) of SYM becomes infinite as N → ∞ {\displaystyle N\rightarrow \infty } it becomes equivalent to an 11-dimensional theory known as matrix theory .
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10 6 M MM megamolar 10 −9 M nM nanomolar 10 9 M GM gigamolar 10 −12 M pM picomolar 10 12 M TM teramolar 10 −15 M fM femtomolar 10 15 M PM petamolar 10 −18 M aM attomolar 10 18 M EM examolar 10 −21 M zM zeptomolar 10 21 M ZM zettamolar 10 −24 M yM yoctomolar 10 24 M YM yottamolar 10 −27 M rM rontomolar 10 27 M RM ronnamolar 10 −30 M