Mathematically, the unification is accomplished under an SU ( 2 ) × U ( 1 ) gauge group.

While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU ( 3 ) and SU ( 2 ) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U ( 1 ) which in principle allows for arbitrary charge assignments.

SU ( 5 ) is the simplest GUT.

The fact that all currently known ( 2009 ) matter particles fit nicely into three copies of the smallest group representations of SU ( 5 ) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.

Here, the unification of matter is even more complete, since the irreducible spinor representation 16 contains both the and 10 of SU ( 5 ) and a right-handed neutrino, and thus the complete particle content of one generation of the extended standard model with neutrino masses.

The boson matrix for SO ( 10 ) is found by taking the 15x15 matrix from the 10 + 5 representation of SU ( 5 ) and adding an extra row and column for the right handed neutrino.

It turns out that including left and right-handed 4x4 quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU ( 2 ) and so has an extra neutral boson and two more charged bosons.

The renormalization group running of the three gauge couplings in the Standard Model has been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU ( 5 ) or SO ( 10 ) GUTs, which are precisely the GUT groups which lead to a simple fermion unification.

Some GUT theories like SU ( 5 ) and SO ( 10 ) suffer from what is called the doublet-triplet problem.

As an approach to the unification of the forces, it is straightforward to apply the Kaluza – Klein theory in an attempt to unify gravity with the strong and electroweak forces by using the symmetry group of the Standard Model, SU ( 3 ) × SU ( 2 ) × U ( 1 ).

For example, the Lie algebra of SU ( n ) is written as.

* The group U ( 1 )× SU ( 2 )× SU ( 3 ) is a Lie group of dimension 1 + 3 + 8 = 12 that is the gauge group of the Standard Model in particle physics.

It is the study of the SU ( 3 ) Yang – Mills theory of color-charged fermions ( the quarks ).

QCD is a gauge theory of the SU ( 3 ) gauge group obtained by taking the color charge to define a local symmetry.

If one considers a version of QCD with N < sub > f </ sub > flavors of massless quarks, then there is a global ( chiral ) flavor symmetry group SU < sub > L </ sub >( N < sub > f </ sub >) × SU < sub > R </ sub >( N < sub > f </ sub >) × U < sub > B </ sub >( 1 ) × U < sub > A </ sub >( 1 ).

The chiral symmetry is spontaneously broken by the QCD vacuum to the vector ( L + R ) SU < sub > V </ sub >( N < sub > f </ sub >) with the formation of a chiral condensate.

In 2009, SU completed the largest capital campaign in the university's history, raising almost $ 169 million and surpassing the original campaign goal by almost $ 20 million.

The Arthur W. Perdue Foundation donated $ 8 million for the building, the largest gift for a capital project in SU history.

It used Riley's 110 hp ( 82 kW ) 2. 5 L ( 2443 cc ) twin-cam, " Big Four " straight-4 engine fitted with twin SU carburettors and had a separate all steel chassis with coil spring rear ( this was changed to leaf springs towards the end of production ) and front torsion bar independent suspension.

The full size Jaguar Mark X saloon ( pronounced " mark ten ") used Jaguar's new independent rear suspension and a triple SU carburettor version of the 3. 8-litre XK engine.

Seattle University ( SU ) is a Jesuit Catholic university located in the First Hill neighbourhood and Squire Park portion of the Central District of Seattle, Washington, USA.

Syracuse University, commonly referred to as Syracuse, ' Cuse, or SU, is a private research university located in Syracuse, New York, United States.

Streeling University ( also known as SU ) is a fictional university in the Foundation Universe, modeled after Harvard University

Moscow Institute of Physics and Technology ( State University ) (), abbreviated MIPT, MIPT ( SU ) or informally Phystech ( alternative transliterations: MFTI, Fizteh, Fiztek ; ) is a leading Russian university, originally established in the Soviet Union.

Silliman University ( also referred to as Silliman or SU ) is a private research university located in Dumaguete, Philippines.

SU is an interdisciplinary university whose mission is to assemble, educate and inspire a cadre of leaders who strive to understand and facilitate the development of exponentially advancing technologies to address humanity's grand challenges.

The Students ' Union ( SU ) was first housed in the university college's original Chapel and had a bar where the Baptismal font used to be.

The University of Sindh () () informally known as Sindh University ( abbreviated SU or USindh ) is the second oldest university in Pakistan accredited by the Higher Education Commission of Pakistan.

* Vought SU, a US Navy Scout aircraft

Due to American pressure the new features were open headlights, different switches, and some de-tuning ( with a downgrade of twin Zenith-Stromberg carbs from the original triple SU carbs ) for US models.

* Jaguar E-Type Series 1 4. 2-1964-68, painted gold, 3 × SU HD8 carburettors ( from 1967 US specification E-Types used 2 × Zenith-Stromberg 175 CDSE carburettor for reduced emissions )

* Jaguar E-Type Series 2-1968-70, 3 × SU HD8 carburettors ( US specification E-Types used 2 × Zenith-Stromberg 175 CDSE carburettor for reduced emissions )

From 1977, 2 × SU HIF7 carburettors, US market from May 1978 Bosch-Lucas L-Jetronic electronic injection

From 1977, 2 × SU HIIF7 carburettors, US market ( VDP only ) from May 1978 Bosch-Lucas L-Jetronic

In 1965, Moo-Young Han with Yoichiro Nambu and Oscar W. Greenberg independently resolved the problem by proposing that quarks possess an additional SU ( 3 ) gauge degree of freedom, later called color charge.

The only difference is again that in the QCD one is dealing with SU ( 3 ) matrices, and that one is dealing with a " fluctuating " quantity.

Investing and partnering with Seattle and the SU neighborhood are part of the Jesuit Catholic mission of education for service and social justice.

SU is organized into 13 schools and colleges, with nationally recognized programs in information studies and library science, architecture, communications, business administration, public administration, engineering and the College of Arts and Sciences. The Foundation for Individual Rights in Education, or FIRE, listed Syracuse University as 2nd among the " 12 Worst Colleges for Free Speech in 2012 ".

In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes ( this is a consequence of the isomorphism of SU ( 2 ) with SO ( 3 )).

The Union supports a wide range of clubs and societies, with over 40 in total ranging from the Rock Society to Dance @ SU.

Thus the topology of the group SL ( n, C ) is the product of the topology of SU ( n ) and the topology of the group of hermitian matrices of unit determinant with positive eigenvalues.

The group Spin ( 3 ) is isomorphic to the special unitary group SU ( 2 ); it is also diffeomorphic to the unit 3-sphere S < sup > 3 </ sup > and can be understood as the group of unit quaternions ( i. e. those with absolute value 1 ).

The special unitary group of degree n, denoted SU ( n ), is the group of n × n unitary matrices with determinant 1.

* M has a Kähler metric with global holonomy contained in SU ( n ).

* M has a Kähler metric with local holonomy contained in SU ( n ).

Abelian surfaces have a Ricci flat metric with holonomy strictly smaller than SU ( 2 ) ( in fact trivial ) so are not Calabi – Yau manifolds according to such definitions.

More generally, a flux-free compactification on an n-manifold with holonomy SU ( n ) leaves 2 < sup > 1 − n </ sup > of the original supersymmetry unbroken, corresponding to 2 < sup > 6 − n </ sup > supercharges in a compactification of type II supergravity or 2 < sup > 5 − n </ sup > supercharges in a compactification of type I.

The new Scimitar GT car retained the straight-six engine from the Sabre, but with triple SU carburettors as standard it now produced 120 bhp and propelled the car to a top speed of 117 mph.

When this occurs SU ( 5 ) is spontaneously broken to the subgroup of SU ( 5 ) commuting with the group generated by Y.