Mathematical Physics

In 1953 as a research associate at Brookhaven National Laboratory, Mills coauthored with Chen Ning Yang a landmark scientific paper in which they proposed the Yang-Mills theory, a generalization of Maxwell's equations that seeks to describe the behavior of elementary particles and explain the electromagnetic and nuclear forces.

is a cornerstone of the mathematical formulation of quantum mechanics

relates the time derivative of the expectation values of the position and momentum operators

It is used extensively in quantum field theory to reduce arbitrary products of creation

The adiabatic theorem is a concept in quantum mechanics

In quantum mechanics, the Hellmann-Feynman theorem relates the derivative of the total energy with respect to a parameter

Noether's second theorem relates symmetries of an action functional with a system of differential equations

all stationary black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity

is a kinetic phenomenon of classical mechanics

The Clausius theorem, also known as the Clausius inequality, states that for a thermodynamic system

In fluid mechanics, the Taylor-Proudman theorem

describes the spacetime geometry around a mass that is electrically charged and rotating

In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor

is a metric that describes a homogeneous, isotropic, expanding

is a Hamiltonian formulation of general relativity

is the main mathematical description of spacetime in the absence of gravitation

are constitutive relations for a superconductor

is a function used to handle the effects of velocity-proportional frictional forces in Lagrangian mechanics

In analytical mechanics, the mass matrix is a symmetric matrix

In quantum field theory, self-energy

used for adding angular momentum values in quantum mechanics

appear when studying an idealized paramagnetic material in statistical mechanics

Prigogine's theorem is a theorem of non-equilibrium thermodynamics, originally formulated by Ilya Prigogine.

In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis.

In quantum information and computation, the Solovay-Kitaev theorem says that if a set of single-qubit quantum gates generates a dense subgroup of SU(2), then that set can be used to approximate any desired quantum gate with a short sequence of gates that can also be found efficiently.

The transport theorem (or transport equation, rate of change transport theorem or basic kinematic equation or Bour's formula

In kinematics, the acceleration of a particle moving along a curve in space is the time derivative of its velocity.

he received a doctoral degree for his award-winning manuscript "Zur mathematischen Theorie electrischer Ströme"

was an American mathematical physicist

best remembered for the development of the Ising model

the mathematical theory of elasticity

was an English mathematical physicist famous for research on elasticity

renowned for his research in mathematical physics and numerical analysis

known for important contributions to topology, functional analysis, mathematical physics

Siacci also studied theoretical mechanics

Galileo Galilei was an Italian scientist who formulated the basic law of falling bodies, which he verified by careful measurements.

Mathieu's main work, after his initial interest in pure mathematics, was in mathematical physics

Ising-type models in mathematical physics

a bachelor's degree in mathematical physics

professor of theoretical physics at the University of Bristol

an exact solution to the Einstein field equation of general relativity

was a British mathematical physicist

theory of phase transitions and critical phenomena of fluids

The Kerr metric is an exact solution of the Einstein field equations of general relativity

phenomenology of particle production in high-energy particle accelerators

an Austrian theoretical physicist who made major contributions to statistical mechanics and its relation to quantum mechanics

a French mathematician and politician working primarily on partial differential equations, Riemannian geometry and mathematical physics

author of mathematics and physics textbooks

he is principally known for his studies in hydrodynamics

specializing in differential equations, determinants, and mathematical physics

His primary research fields were astrophysics, nuclear physics, quantum mechanics, mathematical physics, and statistics

contributions to the theory of hydrodynamics, vibration, light, and heat

His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer

His early research focused on hydromechanics.

was a British mathematician, mathematical physicist and engineer

rewrote Maxwell's equations in the form commonly used today

made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter

wrote a number of articles that announced and explained Einstein's theory of general relativity

was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation

a founding father of modern aero- and hydrodynamics

was a Swiss mathematician best known for his work in physics, the Balmer series of the hydrogen atom

theoretical physicist, and mathematician who made major contributions to cosmology and astrophysics

He was responsible for crucial advances in aerodynamics characterizing supersonic and hypersonic airflow

was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripple marks in sand and water

He originated the pioneering theory that the universe is expanding, governed by a set of equations he developed known as the Friedmann equations

He made important contributions in many areas of physics, including quantum theory, the theory of radiation and stellar evolution

he made major contributions to celestial mechanics

Much of his research in the 1930s was concerned with the theory of relativity and cosmology

He is best known for his work on quantum mechanics in the early 1920s

known for the Kaluza-Klein theory, involving field equations in five-dimensional space-time

originating Stefan's law in 1879

He is known for the de Sitter universe, which is a cosmological model that was named after him

made contributions to the fields of statistical mechanics and statistical thermodynamics with her husband Paul Ehrenfest

he gave completely general integral solutions to the differential equations of electromagnetism

established the fundamentals of the quantum mechanical theory of magnetism, crystal field theory and ligand field theory

He has also worked on mathematical physics and probability theory.

related theories in probability theory and mathematical physics

His work concentrates on geometric aspects of mathematical physics

currently working in quantum field theory

In 1669, he published two scientific treatises: Exercitationes mechanicae and De resistentia solidorum, the latter of which is considered his masterpiece.

Huygens's horological research led to an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th-century works on mechanics.

contributed to early stress analysis

supplementary forces that are detected in a rotating frame of reference

studied in particular continuum mechanics

main scientific work is Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam ("Mathematical Elements of Natural Philosophy, Confirmed by Experiments; or, an Introduction to Newtonian Philosophy"),

Jakob Hermann (16 July 1678-11 July 1733) was a mathematician who worked on problems in classical mechanics.

envisage sous un point de vue nouveau la communication du mouvement

He also made important contributions to the mathematical theory of electrodynamics

was a German theoretical and mathematical physicist who co-founded and made significant contributions to quantum mechanics and quantum field theory

The general properties of the potential function are subsequently developed and applied to electricity and magnetism.

He held the chair of mathematical physics at the University of Turin

Pierre-Louis Maupertuis was a French mathematician who is most famous for formulating the principle of least action.

to study quantum corrections to classical statistical mechanics

She received her Ph.D. in Mathematical Physics at Princeton University

is an American mathematical physicist

working in the fields of mathematical physics, statistical mechanics, functional analysis and probability theory

Andreas Floer was a German mathematician best known for his work in symplectic topology and mathematical physics.

She is known for her foundational work in quantum mechanics and computer algebra

working in representation theory, algebraic geometry, and mathematical physics

His research has spanned representation theory, mathematical physics, algebraic geometry, Lie groups and Lie algebras

working on mathematical physics and dynamical systems theory

he promoted research on various aspects of modern mathematical physics

is a mathematical physicist known for his contributions to statistical physics, statistical mechanics, and many other fields of mathematics and physics

He also made major contributions to applied mathematics and physics

who worked in geometry and mathematical physics

Darwin made a major study of the three-body problem

topics in applied mathematics and physics

his research interests were now turning towards mathematical physics rather than to pure mathematics

Mark Aronovich Naimark was a Ukrainian mathematician who worked in functional analysis and mathematical physics.

on the application of quantum mechanics to the physics of crystals

The main mathematical topic on which Ball did research was dynamics, in particular the theory of screws.

mathematical physics

theory of relativity

analytical mechanics

mathematical physicist

theoretical physicist

theoretical physicist

Poinsot was the inventor of geometrical mechanics

He also did much to systematise the mathematical theory of mechanics

Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics. == Education and career == Kochen was born in Antwerp, Belgium, and escaped the Nazis with his family, thanks to a courageous Norwegian ship captain.

The Ising model (or Lenz-Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics.

In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice.

The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two states and the irreversible work along an ensemble of trajectories joining the same states.

While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag's theorem.

The Reeh-Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961.

The theorem is usually interpreted to mean that the graviton (j = 2) cannot be a composite particle in a relativistic quantum field theory.

In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations.

In quantum field theory and statistical mechanics, the Hohenberg-Mermin-Wagner theorem or Mermin-Wagner theorem (also known as Mermin-Wagner-Berezinskii theorem or Mermin-Wagner-Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2.

The Bohr-Van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero.

In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in a nearly-ideal gas of molecules.

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies.

The fluctuation-dissipation theorem (FDT) or fluctuation-dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance.

In statistical mechanics, Boltzmann's entropy formula (also known as the

In the statistical physics of spin glasses and other systems with quenched disorder, the

In theoretical physics, the Coleman-Mandula theorem is a no-go theorem

twentieth century and was used in the development of the third law of thermodynamics.

In thermodynamics, the Onsager reciprocal relations express the

In fluid mechanics, Kelvin's circulation theorem states:In a barotropic

In classical mechanics, Bertrand's theorem states that among central-force

In quantum mechanics, Kramers' theorem or Kramers' degeneracy theorem

Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body

In classical mechanics, the shell theorem gives gravitational simplifications

The Kutta-Joukowski theorem is a fundamental theorem in aerodynamics that relates the lift per unit span of an airfoil

plane figure theorem) states that for a planar lamina the moment of inertia about an axis perpendicular to the plane of the

In electrodynamics, Poynting's theorem is a statement of conservation

of the past, then, under specific assumptions drawn from quantum mechanics and relativity, so must some elementary particles. That is

In kinematics, Chasles' theorem, or Mozzi-Chasles' theorem

magnitudes of three coplanar, concurrent and non-collinear force vectors, which keeps an object in static equilibrium

Clairaut's theorem characterizes the surface gravity on a viscous rotating ellipsoid in hydrostatic

The Borde-Guth-Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on

In physics, the optical theorem is a general law of wave scattering theory, which relates the zero-angle scattering amplitude

In kinematics, König's theorem or König's decomposition is

Anupam Garg, is a mathematical inequality fulfilled by all macrorealistic physical theories. Here, macrorealism (macroscopic realism) is

In physics, the scallop theorem states that a swimmer that performs a reciprocal

In optics, the Ewald-Oseen extinction theorem, sometimes

The Shockley-Ramo theorem is a method for calculating the electric current induced by a charge moving in the vicinity of an electrode. Previously

In general relativity, Buchdahl's theorem, named after Hans Adolf Buchdahl

In solid mechanics, it is common to analyze the properties of beams

In the linear theory of elasticity Clapeyron's theorem states that the potential

In physics and in particular in the theory of magnetism, an antidynamo theorem is one of several results

(but not necessarily the existence) of a solution to Maxwell's equations, if the boundary conditions provided satisfy

elementary particles

In relativistic physics, a velocity-addition formula is an equation that

The Lorentz factor or Lorentz term (also known as the gamma factor)

The classical rocket equation, Tsiolkovsky rocket equation, or ideal rocket

the formula in 1957, is an equation which expresses the linear response of an observable quantity due to a time-dependent

or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when

In quantum mechanics, the Franke-Gorini-Kossakowski-Sudarshan-Lindblad

In general relativity, a black brane is a solution of the Einstein

Eugene Paul Wigner was a Hungarian-American theoretical physicist and mathematician who won a Nobel prize for his contributions to the theory of the atomic nucleus and elementary particles.

Wilhelm Oseen was a Swedish mathematician who worked in fluid dynamics.

Edward Nelson was an American mathematician who won the Steele Prize for applying probability to quantum field theory. He wrote several classic texts on the topic. In the latter part of his career he studied mathematical logic.

Edward Witten is an American mathematician who won a Fields Medal for his work on quantum field theory.

Franz Rellich was an Austrian-German mathematician who made important contributions in mathematical physics, particular in quantum mechanics.

Gustav Herglotz was a Czech-born German mathematician best known for his works on the theory of relativity and seismology.

Kirchhoff was a mathematical physicist best known for his laws on the flow of electric current.

Heinrich Weber was a German mathematician whose main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.

Paul Dirac is famous as the creator of the complete theoretical formulation of quantum mechanics.

Pierre Varignon was a French mathematician who worked on graphical statics and mechanics.

Wilhelm Magnus was a German American mathematician who worked in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.

Max Born was a Polish-born mathematician who worked in Cambridge and received the Nobel Prize for Physics in 1954 for his work on Quantum Mechanics.

Rudolf Clausius did important work in thermodynamics.

Hendrik Lorentz is best known for his work on electromagnetic radiation and the FitzGerald-Lorentz contraction. He developed the mathematical theory of the electron.