Mathematical physics

study of algorithms that use numerical approximation for the problems of mathematical analysis

physical theory of quantized one-dimensional objects with conformal symmetry, which can describe gravitation, gauge theory and other phenomena

fundamental principle in quantum physics

theoretical framework combining classical field theory, special relativity, and quantum mechanics

use of mathematics to solve physics problems

mathematical transform that expresses a function of time as a function of frequency

the integral transform ∫₀^∞ d𝑠 𝑓(𝑡)⁢exp(−𝑠𝑡)

calculus of vector-valued functions

physical quantity, represented by a number or tensor, that has a value for each point in space-time

space-time coordinate transformation that conserves the form of Maxwell’s equations

vectors that map to their scalar multiples, and the associated scalars

differential equation that contains unknown multivariable functions and their partial derivatives

classical mechanics problem of three massive point particles interacting via Newtonian gravity; special case of the 𝑛‐body problem for 𝑛=3

lowest possible energy of a quantum system or field

formulation of classical mechanics in terms of phase space and Hamiltonian function

fundamental physics principle stating that physical solutions of linear systems are linear

branch of mathematics regarding periodic and continuous signals

formalism of mechanics based on the least action principle

matrices important in quantum mechanics and the study of spin

relativistic wave equation in quantum mechanics

partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics

shorthand notation for tensor operations

physical quantity

idealized concept of a pendulum

procedure to construct a quantum system whose classical limit corresponds to a given classical system

physical theory having a gauge symmetry

theorem that the time evolution of the expectation value of a quantum observable is proportional to that of the commutator between the observable and the Hamiltonian (plus that of any explicit time dependence of the operator, if any)

mathematical structures that allow quantum mechanics to be explained

Green's functions

in Riemannian geometry, the coefficient of the Levi-Civita connection of a Riemannian metric

thumb|500px|Tractrix created by the end of a pole (lying flat on the ground). Its other end is first pushed then dragged by a finger as it spins out to one side.

Riemannian manifold with SU(n) holonomy

Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.

matrix representing a Euclidean rotation

mathematical methods used to find an approximate solution to a problem which cannot be solved exactly

formal sum or integral over all histories of a quantum system

vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star

physical theory describing classical fields

involutive transformation on real-valued convex functions of one real variable

pendulum with another pendulum attached to its end

In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are continuously differentiable.

quantum mechanics

branch of mathematic studying harmonic functions

method for finding approximate solutions to linear differential equations with spatially varying coefficients

functional of dynamical variables whose variation yields the equations of motion in Lagrangian mechanics

partial differential equation used in physics

group of unitary matrices with determinant of 1

mathematical concept

conjectured relation between pairs of Calabi–Yau manifolds; situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory

technique in algebra in which the original variables are replaced with functions of other variables

In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum. In quantum mechanics, an observable is described by a linear operator. For example, these operators might represent submitting the system to various electromagnetic fields and eventually reading a value.

formula that describes the transition rate from one energy eigenstate of a quantum system into other energy eigenstates

award conferred by the American Physical Society

type of stochastic neural network

coefficients in angular momentum eigenstates of quantum systems

quantum field theory enjoying conformal symmetry

Wick-rotated time coordinates in relativistic field theory

material state characterized by magnetic disorder

In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. Propagators may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called ''(causal) Gre

quantum mechanics taking into account particles near or at the speed of light