TY - CHAP
T1 - A new nonformal noncommutative calculus
T2 - Associativity and finite part regularization
AU - Omori, Hideki
AU - Maeda, Yoshiaki
AU - Miyazaki, Naoya
AU - Yoshioka, Akira
PY - 2008/10
Y1 - 2008/10
N2 - We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W2 as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.
AB - We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W2 as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.
KW - Transcendental calculus
KW - Weyl algebra
UR - http://www.scopus.com/inward/record.url?scp=66249124633&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=66249124633&partnerID=8YFLogxK
M3 - Chapter
AN - SCOPUS:66249124633
SN - 9782856292587
T3 - Asterisque
SP - 267
EP - 297
BT - Differential Geometry, Mathematical Physics, Mathematics and Society Part 1
ER -