Pseudovector


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pseudovector

[¦sü·dō′vek·tər]
(physics)
A quantity which transforms as a vector under space rotations but which transforms as a vector, together with a change in sign, under a space inversion. Also known as axial vector.
A quantity which transforms as a four-vector under Lorentz transformations, but with an additional sign change under space reflection or time reflection or both.

Pseudovector

 

(or axial vector), a vector in an oriented space that is transformed into the opposite vector when the orientation of the space is reversed. An example of a pseudovector is the vector product of two vectors.


Pseudovector

 

a vector determined to within an arbitrary numerical factor (vector direction). For example, the homogeneous coordinates x1, x2, x3, x4 of a point in three-dimensional space with a fixed coordinate system can be considered as the components (coordinates) of a four-dimensional pseudovector.

References in periodicals archive ?
The masses of the scalar, vector, pseudoscalar, and pseudovector for B, [B.sub.s], D, and [D.sub.s] mesons have been calculated in the three-dimensional space and in the higher dimensional space in Tables 2-6.
[95] [72] [81] [96] D 2.289 2.318 [+ or -] 2.316 2.364 2.357 0.029 [D.sub.s] 2.350 2.318 2.372 2.437 2.412 B 5.700 5.710 5.657 5.776 5.740 [B.sub.s] 5.720 -- 5.719 5.811 5.776 Meson [88, 89] [73, 74] N=4 N=5 D 2.357[89] 2.539[73] 2.374 2.459 [D.sub.s] 2.438[89] 2.311[73] 2.427 2.505 B 5.730[88] 5.745[74] 5.736 5.815 [B.sub.s] 5.812[88] 5.843[74] 5.785 5.856 Table 5: Masses for pseudovector ([sup.2S+1][L.sub.j] = [sup.1][P.sub.1]) mesons in GeV.
where x is the pseudovector product in [R.sup.3.sub.1].
where x is the pseudovector product in the space [R.sup.3.sub.1].
The term [A.sub.ik][A.sup.ik] here, being expressed through the space rotation angular velocity pseudovector [[OMEGA]*.sup.i], is
Assuming the space rotating in xy plane (only the components [A.sup.12] = -[A.sup.21] are non-zeroes) and replacing the tensor [A.sup.ik] with the space rotation angular velocity pseudovector [[OMEGA].sub.*m] in the form [[epsilon].sub.mik][[OMEGA].sub.*m] = 1/2 [[epsilon].sub.mik][[epsilon].sub.mpq][A.sup.pq] = 1/2 ([[delta].sup.i.sub.p][[delta].sup.k.sub.q] - [[delta].sup.k.sub.p][[delta].sup.i.sub.q])[A.sup.pq] = [A.sup.ik], we obtain
The polyvector X contains not only the vector part [x.sup.[mu]][[gamma].sub.[mu]], but also a scalar part [sigma], tensor part [x.sup.[mu]v] [[gamma].sub.[mu]][conjunction] [[gamma].sub.v], pseudovector part [x.sup.[mu]] I [[gamma].sub.[mu]] and pseudoscalar part [sigma]I.
When calculating the quadratic forms [|X|.sup.2] and [|dX|.sup.2] one obtains in 4-dimensional spacetime with pseudo euclidean signature (+ ) the minus sign in front of the squares of the pseudovector and pseudoscalar terms.