In quantum mechanics, an antisymmetrizer A {\displaystyle {\mathcal {A}}} (also known as antisymmetrizing operator) is a linear operator that makes a wave...
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tensor may be antisymmetrized or symmetrized, and there is according notation. We demonstrate the notation by example. Let's antisymmetrize the type-(0...
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Penrose graphical notation (section Antisymmetrization)
thick zig-zag or wavy bar crossing the index lines horizontally. Antisymmetrization of indices is represented by a thick straight line crossing the index...
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vector; the current, Jα, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂α is the partial derivative with respect to the coordinate...
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exchange of particles and can be expanded in terms of permanents. Antisymmetrizer Electron orbital Fock space Quantum electrodynamics Quantum mechanics...
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a symmetric function in n {\displaystyle n} variables. Similarly, antisymmetrization converts any function in n {\displaystyle n} variables into an antisymmetric...
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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...
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\nu }J_{\mu \nu }\right)\psi (x')\\\end{aligned}}} After properly antisymmetrizing, one obtains the generator of symmetries J μ ν {\displaystyle J_{\mu...
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{\displaystyle f} can be recovered if both its symmetrization and antisymmetrization are known is when n = 2 {\displaystyle n=2} and the abelian group...
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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...
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generalization is consistent with the above definition involving antisymmetrization. Another generalization related to the exterior product is the commutator...
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_{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 ] ...
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Conditionally convergent series Riemann series theorem Lévy–Steinitz theorem Antisymmetrizer Identical particles Levi-Civita symbol Permutable prime Bit-reversal...
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}\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 −...
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{\displaystyle |\Psi \rangle } is constructed using a symmetrizer or antisymmetrizer operator. Particles that form symmetric states are called bosons and...
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totally antisymmetric part of the tensor. It is thus equivalent to antisymmetrization followed by applying the Hodge star. The unit volume form ω = ⋆ 1...
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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 , ⋯...
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stimulated electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included, and the Pauli exclusion principle...
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tensor and the brackets and parentheses on the indices denote the antisymmetrization and symmetrization operators, respectively. If there is nonzero torsion...
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identical particles are fermions, the n-particle states are vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H (see symmetric...
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while the Lie derivative is linear in neither argument. Note that the antisymmetrized covariant derivative ∇uv − ∇vu, and the Lie derivative Luv differ by...
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Igor A. Misurkin (2001). "Ionization potentials within semiempirical antisymmetrized product of strictly localized geminals approach". International Journal...
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{\mathcal {S}}} for symmetrizer, and A {\displaystyle {\mathcal {A}}} for antisymmetrizer. For bosons, the many-body wave function must be symmetrized, Ψ B [...
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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...
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the type (4,4) generalized Kronecker delta in 4 dimensions, in full antisymmetrization. If ε α … β {\displaystyle \ \varepsilon _{\alpha \dots \beta...
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{\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...
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orbitals. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals. There are two main ways...
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product of two variables, the commutator. To see this, examine the (antisymmetrized) product of two matrices A and B in the correspondence limit, where...
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In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product. The Moyal bracket was developed in about 1940...
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Olympic gymnast Moyal bracket, in physics, the suitably normalized antisymmetrization of the phase-space star product Moyal product, in mathematics, perhaps...
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