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The number of ways to link an X to two external lines is 4 × 3, and either X could link up to either pair, giving an additional factor of 2. The remaining two half-lines in the two X s can be linked to each other in two ways, so that the total number of ways to form the diagram is 4 × 3 × 4 × 3 × 2 × 2, while the denominator is 4! × 4 ...
Standard Model of Particle Physics. The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces.
It is often preferable to work directly with these as they contain all the information that the full correlation functions contain since any disconnected diagram is merely a product of connected diagrams. By excluding other sets of diagrams one can define other correlation functions such as one-particle irreducible correlation functions.
a labeling V 2 → Hom(V,V) associating each degree-2 vertex to a linear transformation. Note that V 2 and V n should be considered as distinct sets in the case n = 2. A framed trace diagram is a trace diagram together with a partition of the degree-1 vertices V 1 into two disjoint ordered collections called the inputs and the outputs.
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
Adding a scalar multiple of one column to another column does not change the value of the determinant. This is a consequence of multilinearity and being alternative: by multilinearity the determinant changes by a multiple of the determinant of a matrix with two equal columns, which determinant is 0, since the determinant is alternating.
This nonzero value underlies the Higgs mechanism of the Standard Model. This value is given by v = 1 / 2 G F 0 = 2 M W / g ≈ 246.22 G e V {\displaystyle v=1/{\sqrt {{\sqrt {2}}G_{F}^{0}}}=2M_{W}/g\approx 246.22\,{\rm {GeV}}} , where M W is the mass of the W Boson, G F 0 {\displaystyle G_{F}^{0}} the reduced Fermi constant , and g the weak ...
The group SU(2) is the Lie group of unitary 2 × 2 matrices with unit determinant; its Lie algebra is the set of all 2 × 2 anti-Hermitian matrices with trace 0. Direct calculation, as above, shows that the Lie algebra s u 2 {\displaystyle {\mathfrak {su}}_{2}} is the three-dimensional real algebra spanned by the set { iσ k } .