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Robert Mills | |
---|---|

Born | April 15, 1927 |

Died | October 27, 1999 (aged 72) |

Known for | Yang–Mills theory |

Scientific career | |

Fields | Theoretical physics, quantum field theory |

**Robert Laurence Mills** (April 15, 1927 – October 27, 1999) was an American physicist, specializing in quantum field theory, the theory of alloys, and many-body theory. While sharing an office at Brookhaven National Laboratory, in 1954, Chen Ning Yang and Mills proposed a tensor equation for what are now called Yang–Mills fields (this equation reduces to Maxwell's equations as a special case; see gauge theory):

A **physicist** is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies.

In theoretical physics, **quantum field theory** (**QFT**) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics and is used to construct physical models of subatomic particles and quasiparticles.

An **alloy** is a combination of metals and of a metal or another element. Alloys are defined by a metallic bonding character. An alloy may be a solid solution of metal elements or a mixture of metallic phases. Intermetallic compounds are alloys with a defined stoichiometry and crystal structure. Zintl phases are also sometimes considered alloys depending on bond types.

- .

Mills was born in Englewood, New Jersey,^{ [1] } son of Dorothy C. and Frederick C. Mills.^{ [2] } He graduated from George School in Pennsylvania in early 1944. He studied at Columbia College from 1944 to 1948, while on leave from the Coast Guard. Mills demonstrated his mathematical ability by winning the William Lowell Putnam Mathematical Competition in 1948, and by receiving first-class honors in the Tripos. The mathematical ability he displayed there was evident throughout his career as theoretical physicist. He earned a master's degree from Cambridge, and a Ph.D. in Physics under Norman Kroll, from Columbia University in 1955. After a year at the Institute for Advanced Study in Princeton, New Jersey, Mills became Professor of Physics at Ohio State University in 1956. He remained at Ohio State University until his retirement in 1995.^{ [3] }

**Englewood** is a city located in Bergen County, New Jersey, United States. As of the 2010 United States Census, the city had a total population of 27,147, reflecting an increase of 944 (+3.6%) from the 26,203 counted in the 2000 Census, which had in turn increased by 1,353 (+5.4%) from the 24,850 counted in the 1990 Census.

**Frederick Cecil Mills** was an American economist. He was a Professor of Economics at Columbia University in Manhattan from 1919 to 1959. An expert on business cycles, he was also a researcher at the National Bureau of Economic Research from 1925 to 1953. In 1940, he served as President of the American Economic Association.

**George School** is a private Quaker boarding and day high school located on a rural campus near Newtown, Bucks County, Pennsylvania, United States. It was founded at its present site in 1893, and has grown from a single building to over 20 academic, athletic, and residential buildings. Besides the usual college preparatory courses, including an International Baccalaureate program, the school features several distinct programs deriving from its Quaker heritage. These include community service requirements, an emphasis on social justice and environmental concerns, required arts courses, and community-based decision making.

Mills and Yang shared the 1980 Rumford Premium Prize from the American Academy of Arts and Sciences for their "development of a generalized gauge invariant field theory" in 1954.

Founded in 1796, the **Rumford Prize**, awarded by the American Academy of Arts and Sciences, is one of the oldest scientific prizes in the United States. The prize recognizes contributions by scientists to the fields of heat and light. These terms are widely interpreted; awards range from discoveries in thermodynamics to improvements in the construction of steam boilers.

The **American Academy of Arts and Sciences** is one of the oldest learned societies in the United States. Founded in 1780, the Academy is dedicated to honoring excellence and leadership, working across disciplines and divides, and advancing the common good.

Mills was married to Elise Ackley in 1948. Together they had sons Edward and Jonathan, and daughters Katherine, Susan, and Dorothy. The Mills family lived for many years in Columbus, Ohio during Mills' tenure as professor at Ohio State University. The family also spent considerable time during the summer and winter breaks at their property on Echo Lake in Charleston, Vermont. Robert opted to live out his final months at their residence there.

**Columbus** is the state capital of and the most populous city in the U.S. state of Ohio. With a population of 879,170 as of 2017 estimates, it is the 14th-most populous city in the United States and one of the fastest growing large cities in the nation. This makes Columbus the third-most populous state capital in the US and the second-most populous city in the Midwest. It is the core city of the Columbus, OH Metropolitan Statistical Area, which encompasses ten counties. With a population of 2,078,725, it is Ohio's second-largest metropolitan area.

**The Ohio State University**, commonly referred to as **Ohio State** or **OSU**, is a large public research university in Columbus, Ohio. Founded in 1870 as a land-grant university and the ninth university in Ohio with the Morrill Act of 1862, the university was originally known as the **Ohio Agricultural and Mechanical College** (**Mech**). The college began with a focus on training students in various agricultural and mechanical disciplines but it developed into a comprehensive university under the direction of then-Governor Rutherford B. Hayes, and in 1878 the Ohio General Assembly passed a law changing the name to "**The Ohio State University**". It has since grown into the third-largest university campus in the United States. Along with its main campus in Columbus, Ohio State also operates regional campuses in Lima, Mansfield, Marion, Newark, and Wooster.

**Charleston** is a town in Orleans County, Vermont, United States. The population was 895 at the 2000 census. The town contains three unincorporated villages: Charleston, East Charleston and West Charleston.

- Yang C. N., Mills R. L. (1954). "Conservation of Isotopic Spin and Isotopic Gauge Invariance".
*Phys. Rev.***96**: 191–195. Bibcode:1954PhRv...96..191Y. doi:10.1103/PhysRev.96.191. - Mills R. L., Yang C. N. (1966). "Treatment of Overlapping Divergences in the Photon Self-Energy Function".
*Prog. Theor. Phys. Sup*.**37**: 507.

The **bibcode** is a compact identifier used by several astronomical data systems to uniquely specify literature references.

In computing, a **Digital Object Identifier** or **DOI** is a persistent identifier or handle used to identify objects uniquely, standardized by the International Organization for Standardization (ISO). An implementation of the Handle System, DOIs are in wide use mainly to identify academic, professional, and government information, such as journal articles, research reports and data sets, and official publications though they also have been used to identify other types of information resources, such as commercial videos.

- ↑ Staff.
*A COMMUNITY OF SCHOLARS: The Institute for Advanced Study Faculty and Members 1930-1980*, p. 292. Institute for Advanced Study, 1980. Accessed November 22, 2015. "Mills, Robert L. 55-56 M(NS), Theoretical Physics Born 1927 Englewood, NJ." - ↑ https://www.college.columbia.edu/cct_archive/feb00/feb00_obituaries.html
- ↑
*The New York Times*. "Dr. Robert Mills, 72, Contributed to Study of Subatomic Particles",*South Florida Sun-Sentinel*, October 31, 1999. Accessed November 2, 2012. "Dr. Mills, who lived in Columbus, was born on April 15, 1927, in Englewood, N.J."

In particle physics, the **electroweak interaction** is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single **electroweak force**. Thus, if the universe is hot enough (approximately 10^{15} K, a temperature not exceeded since shortly after the Big Bang), then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch, the electroweak force split into the electromagnetic and weak force.

In physics, **Kaluza–Klein theory** is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory.

In theoretical physics, **quantum chromodynamics** (**QCD**) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called *color*. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

In particle physics, **quantum electrodynamics** (**QED**) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

In 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 number of positive and negative charged particles, that when opened was found to have more positive than negative particles, or vice versa.

The **Einstein field equations** comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy. First published by Einstein in 1915 as a tensor equation, the EFE relate local *spacetime curvature* with the local energy and momentum within that spacetime.

**Yang–Mills theory** is a gauge theory based on the SU(*N*) group, or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces as well as quantum chromodynamics, the theory of the strong force. Thus it forms the basis of our understanding of the Standard Model of particle physics.

In theoretical physics, the **Rarita–Schwinger equation** is the relativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941.

In differential geometry and mathematical physics, a **spin connection** is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection. It can also be regarded as the gauge field generated by local Lorentz transformations. In some canonical formulations of general relativity, a spin connection is defined on spatial slices and can also be regarded as the gauge field generated by local rotations.

In mathematical physics, a **caloron** is the finite temperature generalization of an instanton.

In theoretical physics, the **BPST instanton** is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu. S. Tyupkin. It is a classical solution to the equations of motion of SU(2) Yang–Mills theory in Euclidean space-time, meaning it describes a transition between two different vacua of the theory. It was originally hoped to open the path to solving the problem of confinement, especially since Polyakov had proven in 1987 that instantons are the cause of confinement in three-dimensional compact-QED. This hope was not realized, however.

**Alternatives to general relativity** are physical theories that attempt to describe the phenomenon of gravitation in competition to Einstein's theory of general relativity.

In physics, a **gauge theory** is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.

In mathematics, any Lagrangian system generally admits gauge symmetries, though it may happen that they are trivial. In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory.

In theoretical physics, **Lovelock's theory of gravity** is a generalization of Einstein's theory of general relativity introduced by David Lovelock in 1971. It is the most general metric theory of gravity yielding conserved second order equations of motion in arbitrary number of spacetime dimensions *D*. In this sense, Lovelock's theory is the natural generalization of Einstein's General Relativity to higher dimensions. In three and four dimensions, Lovelock's theory coincides with Einstein's theory, but in higher dimensions the theories are different. In fact, for *D* > 4 Einstein gravity can be thought of as a particular case of Lovelock gravity since the Einstein–Hilbert action is one of several terms that constitute the Lovelock action.

** N = 4 supersymmetric Yang–Mills** (

In theoretical particle physics, the **gluon field strength tensor** is a second order tensor field characterizing the gluon interaction between quarks.

**Infinite derivative gravity** is a theory of gravity which attempts to remove cosmological and black hole singularities by adding extra terms to the Einstein–Hilbert action, which weaken gravity at short distances.

**Higher Spin Theory** or **Higher Spin Gravity** is a common name for field theories that contain massless fields of spin greater than two. Usually, the spectrum of such theories contains the graviton as a massless spin-two field, which explains the second name. Massless fields are gauge fields and the theories should be (almost) completely fixed by these higher spin symmetries. Higher spin theories are supposed to be consistent quantum theories and, for this reason, to give examples of quantum gravity. Most of the interest in the topic is due to the AdS/CFT correspondence where there is a number of conjectures relating higher spin theories to weakly coupled conformal field theories. It is important to note that only certain parts of these theories are known at present and not many examples have been worked out in detail except some specific toy models.

- Samuel L. Marateck (2003). "Remembering Robert Mills".
*Physics Today*.**56**(10): 14–15. Bibcode:2003PhT....56j..14M. doi:10.1063/1.1628986. - C. N. Yang (2005). "Remembering Robert Mills". In Gerardus 't Hooft.
*50 years of Yang-Mills theory*. World Scientific. ISBN 978-981-238-934-3.

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

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