prepotentialadj.n.

Brit.

/ˌpriːpəˈtɛnʃl/, U.S.

/ˌpripəˈtɛn(t)ʃ(ə)l/

Origin: Formed within English, by derivation. Etymons: pre- prefix, potential adj.

Etymology: < pre- prefix + potential adj. With sense A. 2 compare earlier prepotent adj.

†A. adj.

1. Mathematics. Of a mathematical function: analogous to a potential function but more general in that it can be defined for any number of variables and (in the case of three-dimensional space) its differentiation need not result in an inverse square law of force. Obsolete.

ΚΠ

1875 A. Cayley in Philos. Trans. (Royal Soc.) 165 675 The present Memoir relates to multiple integrals expressed in terms of the (s + 1) ultimately disappearing variables (x..z, w), and the same number of parameters (a..c, e)... Such an integral, in regard to the index ½s + q, is said to be ‘prepotential’, and in the particular case q = −½ to be ‘potential’.

2. Having a prior or superior power; prepotent. Obsolete.

ΘΚΠ

society > authority > power > [adjective] > having great or supreme power

prepotent1468

maximious?1567

all-powerful1597

multipotent1609

magnipotent1727

prepotential1888

1888 Academy 24 Nov. 329/3 What a contrast between those days..and our times of ‘telegraphic ambassadors’ and a prepotential ‘clerkery’!

B. n.

†1. Mathematics. A function analogous to a potential function (see sense A. 1). Obsolete.

ΚΠ

1875 A. Cayley in Philos. Trans. (Royal Soc.) 165 680 The prepotential of the whole surface in regard to the indefinitely near point P is thus equal to the prepotential of the disk.

2. Mathematics and Physics. A mathematical function which, when differentiated in a certain way, produces a potential (potential n. 5a).

ΚΠ

1977 H. Pagels in Physics Lett. B. 70 231/1 The purpose of this note is to make this analogy precise by the introduction of prepotentials for the gauge fields A^a_μ. This is in the same sense that the metric g_μν is a prepotential for the connection Γ^α_μν.

1986 P. C. West Introd. Supersymmetry & Supergravity xv. 129 The solution of the constraints of the relaxed hypermultiplet formulation involves the prepotential ρ_Ai and X^ijkl of dimensions −³/ ₂ and −1 respectively.

2004 Nucl. Physics B. 683 27 We show that some large-N reduced models of these theories are supermatrix models, whose free energy is equivalent to the prepotentials of the original gauge theories.

This entry has been updated (OED Third Edition, March 2007; most recently modified version published online March 2022).

单词	prepotential
释义	prepotentialadj.n. Brit. /ˌpriːpəˈtɛnʃl/, U.S. /ˌpripəˈtɛn(t)ʃ(ə)l/ Origin: Formed within English, by derivation. Etymons: pre- prefix, potential adj. Etymology: < pre- prefix + potential adj. With sense A. 2 compare earlier prepotent adj. †A. adj. 1. Mathematics. Of a mathematical function: analogous to a potential function but more general in that it can be defined for any number of variables and (in the case of three-dimensional space) its differentiation need not result in an inverse square law of force. Obsolete. ΚΠ 1875 A. Cayley in Philos. Trans. (Royal Soc.) 165 675 The present Memoir relates to multiple integrals expressed in terms of the (s + 1) ultimately disappearing variables (x..z, w), and the same number of parameters (a..c, e)... Such an integral, in regard to the index ½s + q, is said to be ‘prepotential’, and in the particular case q = −½ to be ‘potential’. 2. Having a prior or superior power; prepotent. Obsolete. ΘΚΠ society > authority > power > [adjective] > having great or supreme power prepotent1468 maximious?1567 all-powerful1597 multipotent1609 magnipotent1727 prepotential1888 1888 Academy 24 Nov. 329/3 What a contrast between those days..and our times of ‘telegraphic ambassadors’ and a prepotential ‘clerkery’! B. n. †1. Mathematics. A function analogous to a potential function (see sense A. 1). Obsolete. ΚΠ 1875 A. Cayley in Philos. Trans. (Royal Soc.) 165 680 The prepotential of the whole surface in regard to the indefinitely near point P is thus equal to the prepotential of the disk. 2. Mathematics and Physics. A mathematical function which, when differentiated in a certain way, produces a potential (potential n. 5a). ΚΠ 1977 H. Pagels in Physics Lett. B. 70 231/1 The purpose of this note is to make this analogy precise by the introduction of prepotentials for the gauge fields A^a_μ. This is in the same sense that the metric g_μν is a prepotential for the connection Γ^α_μν. 1986 P. C. West Introd. Supersymmetry & Supergravity xv. 129 The solution of the constraints of the relaxed hypermultiplet formulation involves the prepotential ρ_Ai and X^ijkl of dimensions −³/ ₂ and −1 respectively. 2004 Nucl. Physics B. 683 27 We show that some large-N reduced models of these theories are supermatrix models, whose free energy is equivalent to the prepotentials of the original gauge theories. This entry has been updated (OED Third Edition, March 2007; most recently modified version published online March 2022). < adj.n.1875
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