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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 diagrams, or the negation of a spider diagram.
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 multiple wires can go between the same pair of nodes. There are also Hadamard nodes, usually denoted by a yellow box, which always connect to exactly two wires.
Write down the two Young diagrams for the two irreps under consideration, such as in the following example. In the second figure insert a series of the letter a in the first row, the letter b in the second row, the letter c in the third row, etc. in order to keep track of them once they are included in the various resultant diagrams:
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
It is in fact equal to the time evolution operator over a very long time (approaching infinity) acting on momentum states of particles (or bound complex of particles) at infinity. Thus it must be a unitary operator as well; a calculation yielding a non-unitary S-matrix often implies a bound state has been overlooked.
The general unitary group, also called the group of unitary similitudes, consists of all matrices A such that A ∗ A is a nonzero multiple of the identity matrix, and is just the product of the unitary group with the group of all positive multiples of the identity matrix. Unitary groups may also be defined over fields other than the complex ...
Also, the diagram D 3 is the same as A 3, corresponding to a covering map homomorphism from SU(4) to SO(6). In addition to the four families A i, B i, C i, and D i above, there are five so-called exceptional Dynkin diagrams G 2, F 4, E 6, E 7, and E 8; these
For a field F, the generalized special unitary group over F, SU(p, q; F), is the group of all linear transformations of determinant 1 of a vector space of rank n = p + q over F which leave invariant a nondegenerate, Hermitian form of signature (p, q). This group is often referred to as the special unitary group of signature p q over F.