Abstract
The formal use of complex variable (special relativity), the use of complex functions (quantum mechanics, Fourier transform, etc. ), the N dimensional space complessification are well know to physicists. The hypercomplex numbers are seldom considered and, when this is done, the non commutative Hamilton quaternions are generally used. In this report is shown how commutative hypercomplex numbers can be an extension of complex variable and important applications are proposed. The basic concepts of the algebra of hypercomplex numbers and their relation with continuos finite Lie groups are shown. The conditions that allow to extend the function theory of complex variable to hypercomplex numbers systems and to link them to infinite Lie group and physical fields are explained. To conclude all the systems up to 4 elements are given.
Catoni, F
[1]
- ENEA, Casaccia (Italy). Area Energetica
Citation Formats
Catoni, F.
Hypercomplex numbers, functions of hypercomplex variable and physical fields; Sistemi di numeri ipercomplessi, funzioni di variabile ipercomplessa e campi fisici.
Italy: N. p.,
1994.
Web.
Catoni, F.
Hypercomplex numbers, functions of hypercomplex variable and physical fields; Sistemi di numeri ipercomplessi, funzioni di variabile ipercomplessa e campi fisici.
Italy.
Catoni, F.
1994.
"Hypercomplex numbers, functions of hypercomplex variable and physical fields; Sistemi di numeri ipercomplessi, funzioni di variabile ipercomplessa e campi fisici."
Italy.
@misc{etde_10123626,
title = {Hypercomplex numbers, functions of hypercomplex variable and physical fields; Sistemi di numeri ipercomplessi, funzioni di variabile ipercomplessa e campi fisici}
author = {Catoni, F}
abstractNote = {The formal use of complex variable (special relativity), the use of complex functions (quantum mechanics, Fourier transform, etc. ), the N dimensional space complessification are well know to physicists. The hypercomplex numbers are seldom considered and, when this is done, the non commutative Hamilton quaternions are generally used. In this report is shown how commutative hypercomplex numbers can be an extension of complex variable and important applications are proposed. The basic concepts of the algebra of hypercomplex numbers and their relation with continuos finite Lie groups are shown. The conditions that allow to extend the function theory of complex variable to hypercomplex numbers systems and to link them to infinite Lie group and physical fields are explained. To conclude all the systems up to 4 elements are given.}
place = {Italy}
year = {1994}
month = {Sep}
}
title = {Hypercomplex numbers, functions of hypercomplex variable and physical fields; Sistemi di numeri ipercomplessi, funzioni di variabile ipercomplessa e campi fisici}
author = {Catoni, F}
abstractNote = {The formal use of complex variable (special relativity), the use of complex functions (quantum mechanics, Fourier transform, etc. ), the N dimensional space complessification are well know to physicists. The hypercomplex numbers are seldom considered and, when this is done, the non commutative Hamilton quaternions are generally used. In this report is shown how commutative hypercomplex numbers can be an extension of complex variable and important applications are proposed. The basic concepts of the algebra of hypercomplex numbers and their relation with continuos finite Lie groups are shown. The conditions that allow to extend the function theory of complex variable to hypercomplex numbers systems and to link them to infinite Lie group and physical fields are explained. To conclude all the systems up to 4 elements are given.}
place = {Italy}
year = {1994}
month = {Sep}
}