Search results
Results from the WOW.Com Content Network
These points may be joined forming a shape like a spider. Joined points represent an "or" condition, also known as a logical disjunction. A spider diagram is a boolean expression involving unitary spider diagrams and the logical symbols ,,. For example, it may consist of the conjunction of two spider diagrams, the disjunction of two spider ...
An example ZX-diagram. This one has two inputs (wires coming from the left), and three outputs (wires exiting to the right), and hence it represents a linear map from to . ZX-diagrams consist of green and red nodes called spiders, which are connected by wires. Wires may curve and cross, arbitrarily many wires may connect to the same spider, and ...
In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U −1 equals its conjugate transpose U *, that is, if = =, where I is the identity matrix.. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger ( † ), so the equation above is written
Examples of unitary representations arise in quantum mechanics and quantum field theory, but also in Fourier analysis as shown in the following example. Let G = R {\displaystyle G=\mathbb {R} } , and let the complex Hilbert space V be L 2 ( R ) {\displaystyle L^{2}(\mathbb {R} )} .
In mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication.The unitary group is a subgroup of the general linear group GL(n, C), and it has as a subgroup the special unitary group, consisting of those unitary matrices with determinant 1.
For example, renormalization in QED modifies the mass of the free field electron to match that of a physical electron (with an electromagnetic field), and will in doing so add a term to the free field Lagrangian which must be cancelled by a counterterm in the interaction Lagrangian, that then shows up as a two-line vertex in the Feynman diagrams.
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G.The general theory is well-developed in the case that G is a locally compact topological group and the representations are strongly continuous.
The unitary property of the S-matrix is directly related to the conservation of the probability current in quantum mechanics. The probability current density J of the wave function ψ ( x ) is defined as J = ℏ 2 m i ( ψ ∗ ∂ ψ ∂ x − ψ ∂ ψ ∗ ∂ x ) . {\displaystyle J={\frac {\hbar }{2mi}}\left(\psi ^{*}{\frac {\partial \psi ...