Mathematical physics

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 time, or to travel with a certain energy and momentum.

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

Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions.

In mathematics, a matrix function is a function which maps a matrix to another matrix.

In mathematics, the Dirac delta function, or δ function, is a generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that does not change its direction when that linear transformation is applied to it.

The Fourier transform decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the amplitude (or loudness) of its constituent notes.

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations.

In mathematics, the gradient is a generalization of the usual concept of derivative to functions of several variables.

In mathematics the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/).

Mathematical physics refers to development of mathematical methods for application to problems in physics.

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary.

In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.

In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales.

In mathematics, a Green's function is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions.

The group velocity of a wave is the velocity with which the overall shape of the waves' amplitudes—known as the modulation or envelope of the wave—propagates through space.

In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process.

A spin glass is a disordered magnet, where the magnetic spin of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern.

In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics.

There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental forces of nature.

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM).

Schröder's equation, named after Ernst Schröder, is a functional equation with one independent variable: given the function h(x), find the function Ψ(x) such that: Schröder's equation is an eigenvalue equation for the composition operator Ch, which sends a function f(x) to f(h(x)).

In theoretical physics, the composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation.

In mathematics, Fourier analysis (English pronunciation: /ˈfɔərieɪ/) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

In theoretical physics and mathematics, the Wess–Zumino–Witten (WZW) model, also called the Wess–Zumino–Novikov–Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac–Moody algebras.

In mathematics, the Virasoro algebra (named after the physicist Miguel Angel Virasoro) is a complex Lie algebra, the unique central extension of the Witt algebra.

In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations (or BW equations or BWE) are relativistic wave equations which describe free particles of arbitrary spin j, an integer for bosons (j = 1, 2, 3 ...) or half-integer for fermions (j =  1⁄2,  3⁄2,  5⁄2 ...).

In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.

In theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at distance scales comparable to Planck length.

In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields.