In quantum mechanics, an antisymmetrizer A {\displaystyle {\mathcal {A}}} (also known as antisymmetrizing operator) is a linear operator that makes a wave...

tensor may be antisymmetrized or symmetrized, and there is according notation. We demonstrate the notation by example. Let's antisymmetrize the type-(0...

thick zig-zag or wavy bar crossing the index lines horizontally. Antisymmetrization of indices is represented by a thick straight line crossing the index...

vector; the current, Jα, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂α is the partial derivative with respect to the coordinate...

exchange of particles and can be expanded in terms of permanents. Antisymmetrizer Electron orbital Fock space Quantum electrodynamics Quantum mechanics...

a symmetric function in n {\displaystyle n} variables. Similarly, antisymmetrization converts any function in n {\displaystyle n} variables into an antisymmetric...

in use. More generally, irrespective of the number of dimensions, antisymmetrization over p {\displaystyle p} indices may be expressed as T [ a 1 … a p...

\nu }J_{\mu \nu }\right)\psi (x')\\\end{aligned}}} After properly antisymmetrizing, one obtains the generator of symmetries J μ ν {\displaystyle J_{\mu...

{\displaystyle f} can be recovered if both its symmetrization and antisymmetrization are known is when n = 2 {\displaystyle n=2} and the abelian group...

characteristic of K is 0, one can also establish the isomorphism by antisymmetrizing. Define functions fk : V × ⋯ × V → Cl(V, Q) by f k ( v 1 , … , v k...

generalization is consistent with the above definition involving antisymmetrization. Another generalization related to the exterior product is the commutator...

_{1}}^{[\alpha _{1}}\cdots \delta _{\beta _{p}}^{\alpha _{p}]},} and acts as an antisymmetrizer on p indices: δ β 1 ⋯ β p α 1 ⋯ α p A β 1 ⋯ β p = A [ α 1 ⋯ α p ] ...

Conditionally convergent series Riemann series theorem Lévy–Steinitz theorem Antisymmetrizer Identical particles Levi-Civita symbol Permutable prime Bit-reversal...

}\right),\end{aligned}}} where square brackets conventionally denote antisymmetrization over bracketed indices, i.e. g α [ β , γ ] ϵ = 1 2 ( g α β , γ ϵ −...

{\displaystyle |\Psi \rangle } is constructed using a symmetrizer or antisymmetrizer operator. Particles that form symmetric states are called bosons and...

totally antisymmetric part of the tensor. It is thus equivalent to antisymmetrization followed by applying the Hodge star. The unit volume form ω = ⋆ 1...

Identities (FI) (evocative of the Jacobi identities, but unlike them, not antisymmetrized in all arguments, for N ≥ 2 ): { f 1 , ⋯ ,   f N − 1 ,   { g 1 , ⋯...

stimulated electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included, and the Pauli exclusion principle...

tensor and the brackets and parentheses on the indices denote the antisymmetrization and symmetrization operators, respectively. If there is nonzero torsion...

identical particles are fermions, the n-particle states are vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H (see symmetric...

while the Lie derivative is linear in neither argument. Note that the antisymmetrized covariant derivative ∇uv − ∇vu, and the Lie derivative Luv differ by...

Igor A. Misurkin (2001). "Ionization potentials within semiempirical antisymmetrized product of strictly localized geminals approach". International Journal...

{\mathcal {S}}} for symmetrizer, and A {\displaystyle {\mathcal {A}}} for antisymmetrizer. For bosons, the many-body wave function must be symmetrized, Ψ B [...

eigenfunction is assumed to be describable by a single Slater determinant, an antisymmetrized product of one-electron wave functions (i.e., orbitals). The mean-field...

the type (4,4) generalized Kronecker delta in 4 dimensions, in full antisymmetrization. If   ε α … β   {\displaystyle \ \varepsilon _{\alpha \dots \beta...

{\displaystyle v_{1}\otimes \cdots \otimes v_{r},\quad v_{i}\in V.} The antisymmetrization (or sometimes the skew-symmetrization) of a decomposable tensor is...

orbitals. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals. There are two main ways...

product of two variables, the commutator. To see this, examine the (antisymmetrized) product of two matrices A and B in the correspondence limit, where...

In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product. The Moyal bracket was developed in about 1940...

Olympic gymnast Moyal bracket, in physics, the suitably normalized antisymmetrization of the phase-space star product Moyal product, in mathematics, perhaps...