### Abstract

In this paper we express the disentangling, or the formation of a function of several noncommuting operators using Cauchy's Integral Formula in several complex variables. It is seen that the disentangling of a given function f can be expressed as a contour integral around the boundary of a polydisk where the standard Cauchy kernel is replaced by the disentangling of the Cauchy kernel expressed as an element of the disentangling algebra. This approach to the operational calculus allows for us to develop a "differential calculus" with disentanglings.

Original language | English |
---|---|

Pages (from-to) | 463-488 |

Number of pages | 26 |

Journal | New York Journal of Mathematics |

Volume | 16 |

State | Published - 2010 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Feynman's operational calculi : Using Cauchy's integral formula.** / Nielsen, Lance.

Research output: Contribution to journal › Article

*New York Journal of Mathematics*, vol. 16, pp. 463-488.

}

TY - JOUR

T1 - Feynman's operational calculi

T2 - Using Cauchy's integral formula

AU - Nielsen, Lance

PY - 2010

Y1 - 2010

N2 - In this paper we express the disentangling, or the formation of a function of several noncommuting operators using Cauchy's Integral Formula in several complex variables. It is seen that the disentangling of a given function f can be expressed as a contour integral around the boundary of a polydisk where the standard Cauchy kernel is replaced by the disentangling of the Cauchy kernel expressed as an element of the disentangling algebra. This approach to the operational calculus allows for us to develop a "differential calculus" with disentanglings.

AB - In this paper we express the disentangling, or the formation of a function of several noncommuting operators using Cauchy's Integral Formula in several complex variables. It is seen that the disentangling of a given function f can be expressed as a contour integral around the boundary of a polydisk where the standard Cauchy kernel is replaced by the disentangling of the Cauchy kernel expressed as an element of the disentangling algebra. This approach to the operational calculus allows for us to develop a "differential calculus" with disentanglings.

UR - http://www.scopus.com/inward/record.url?scp=84055182916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84055182916&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 463

EP - 488

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -