Cohl Furey

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Cohl Furey, also known as Nichol Furey, [1] is a Canadian mathematical physicist. [2] [3]

Contents

Career

Furey has a bachelor's degree in mathematics and physics from Simon Fraser University (2005), Master's degree from the University of Cambridge (2006) and a Ph.D in theoretical physics from the University of Waterloo (2015). [4] She was a research fellow at the University of Cambridge from 2016 to 2019 [5] and spent a few months at the African Institute for Mathematical Sciences in Cape Town. Since 2020, she has been at the Humboldt University of Berlin on a Freigeist-Fellowship by the Volkswagen Foundation. [1] [6]

Her main interests are division algebras, Clifford algebras, and Jordan algebras, and their relation to particle physics. Her work focuses on finding an underlying mathematical structure to the Standard Model of particle physics. She is most noted for her work on octonions. [7] [8] [9]

She has worked on attempting to obtain the Standard Model of particle physics from octonionic constructions. [2] [7] [9] In her 2018 paper "SU(3)C × SU(2)L × U(1)Y ( × U(1)X ) as a symmetry of division algebraic ladder operators," [10] according to Quanta Magazine , "she consolidated several findings to construct the full Standard Model symmetry group, SU(3) × SU(2) × U(1), for a single generation of particles, with the math producing the correct array of electric charges and other attributes for an electron, neutrino, three up quarks, three down quarks and their anti-particles. The math also suggests a reason why electric charge is quantized in discrete units — essentially, because whole numbers are." [2] In 2022 together with Mia Hughes, she linked the symmetry breaking in physics to division algebras including octonions. [11]

Media recognition

In 2019, Wired.com listed her in their article "10 Women in Science and Tech Who Should Be Household Names". [12]

Notable publications

Related Research Articles

<span class="mw-page-title-main">Grand Unified Theory</span> Any particle physics model that theorizes the merging of the electromagnetic, weak and strong forces

Grand Unified Theory (GUT) is any model in particle physics that merges the electromagnetic, weak, and strong forces into a single force at high energies. Although this unified force has not been directly observed, many GUT models theorize its existence. If the unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

<span class="mw-page-title-main">Proton decay</span> Hypothetical particle decay process of a proton

In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative.

In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in mathematical physics.

Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (bosons) and particles with half-integer spin (fermions). It proposes that for every known particle, there exists a partner particle with different spin properties. This symmetry has not been observed in nature. If confirmed, it could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics.

G<sub>2</sub> (mathematics) Simple Lie group; the automorphism group of the octonions

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14.

In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa.

<span class="mw-page-title-main">SO(10)</span>

In particle physics, SO(10) refers to a grand unified theory (GUT) based on the spin group Spin(10). The shortened name SO(10) is conventional among physicists, and derives from the Lie algebra or less precisely the Lie group of SO(10), which is a special orthogonal group that is double covered by Spin(10).

<span class="mw-page-title-main">Topological order</span> Type of order at absolute zero

In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.

<span class="mw-page-title-main">Particle physics and representation theory</span> Physics-mathematics connection

There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe.

<span class="mw-page-title-main">Exceptional object</span>

Many branches of mathematics study objects of a given type and prove a classification theorem. A common theme is that the classification results in a number of series of objects and a finite number of exceptions — often with desirable properties — that do not fit into any series. These are known as exceptional objects. In many cases, these exceptional objects play a further and important role in the subject. Furthermore, the exceptional objects in one branch of mathematics often relate to the exceptional objects in others.

In theoretical particle physics, the non-commutative Standard Model, is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard Model.

In mathematics, an octonion algebra or Cayley algebra over a field F is a composition algebra over F that has dimension 8 over F. In other words, it is a 8-dimensional unital non-associative algebra A over F with a non-degenerate quadratic form N such that

Tevian Dray is an American mathematician who has worked in general relativity, mathematical physics, geometry, and both science and mathematics education. He was elected a Fellow of the American Physical Society in 2010.

<span class="mw-page-title-main">Gauge theory</span> Physical theory with fields invariant under the action of local "gauge" Lie groups

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations. Formally, the Lagrangian is invariant.

In particle physics, W′ and Z′ bosons refer to hypothetical gauge bosons that arise from extensions of the electroweak symmetry of the Standard Model. They are named in analogy with the Standard Model W and Z bosons.

In theoretical physics, a mass generation mechanism is a theory that describes the origin of mass from the most fundamental laws of physics. Physicists have proposed a number of models that advocate different views of the origin of mass. The problem is complicated because the primary role of mass is to mediate gravitational interaction between bodies, and no theory of gravitational interaction reconciles with the currently popular Standard Model of particle physics.

<span class="mw-page-title-main">Symmetry in quantum mechanics</span> Properties underlying modern physics

Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general, symmetry in physics, invariance, and conservation laws, are fundamentally important constraints for formulating physical theories and models. In practice, they are powerful methods for solving problems and predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form the correct constraints and the first steps to solving a multitude of problems.

Corinne Alison Manogue is an American physicist who has worked in general relativity, mathematical physics, and physics education. She was elected a Fellow of the American Physical Society in 2005, and was an inaugural Fellow of the American Association of Physics Teachers in 2014.

In mathematics, a bioctonion, or complex octonion, is a pair (p,q) where p and q are biquaternions.

References

  1. 1 2 Deffke, Uta. "The octave magician: Nichol (Cohl) Furey is a researcher at IRIS Adlershof". adlershof.de. Berlin: Adlershof Journal.
  2. 1 2 3 Wolchover, Natalie (July 20, 2018). "The Peculiar Math That Could Underlie the Laws of Nature". Archived from the original on 21 March 2022.
  3. Wolchover, Natalie (December 21, 2018). "The Year in Physics". Archived from the original on 24 April 2022.
  4. "N. Furey - CV" (PDF). Retrieved 2023-08-13.
  5. "Women in STEM: Dr Cohl Furey; University of Cambridge". April 24, 2022. Archived from the original on 24 April 2022.
  6. "Project description: In-depth study into the algebraic structure of elementary particle physics". VolkswagenStiftung. Retrieved 2023-08-13.
  7. 1 2 Furey, Cohl (2012-07-20). "Unified theory of ideals". Physical Review D . 86 (2): 025024. arXiv: 1002.1497 . Bibcode:2012PhRvD..86b5024F. doi:10.1103/PhysRevD.86.025024. S2CID   118458623.
  8. Furey, C. J. (2014-10-07). "Generations: three prints, in colour". Journal of High Energy Physics . 2014 (10): 46. arXiv: 1405.4601 . Bibcode:2014JHEP...10..046F. doi:10.1007/JHEP10(2014)046. S2CID   13813401.
  9. 1 2 Furey, Cohl (2018-10-10). "Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra". Physics Letters B . 785: 84–89. arXiv: 1910.08395 . Bibcode:2018PhLB..785...84F. doi:10.1016/j.physletb.2018.08.032. S2CID   126205768.
  10. Furey, Cohl (2018-05-12). "SU(3)C × SU(2)L × U(1)Y ( × U(1)X ) as a symmetry of division algebraic ladder operators". European Physical Journal C. 78: 375. arXiv: 1806.00612 . doi:10.1140/epjc/s10052-018-5844-7.
  11. Brooks, Michael (August 2022). "Octonions: The strange maths that could unite the laws of nature (=Reality's hidden depths)". New Scientist. 255 (3400): 38–41. doi:10.1016/S0262-4079(22)01494-4.
  12. Dreyfuss, Emily (March 8, 2019). "10 Women in Science and Tech Who Should Be Household Names; WIRED". Archived from the original on 8 March 2022.