### Abstract

In this paper we develop an integral equation satisfied by Feynman's operational calculi in formalism of B. Jefferies and G. W. Johnson. In particular a "reduced" disentangling is derived and an evolution equation of DeFacio, Johnson, and Lapidus is used to obtain the integral equation. After the integral equation is presented, we show that solutions to the heat and Schrodinger's equation can be obtained from the reduced disentanglingand its integral equation. We also make connections between the Jefferies and Johnson development of the operational calculi and the analytic Feynman integral.

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

Title of host publication | Advances in Analysis: Problems of Integration |

Publisher | Nova Science Publishers, Inc |

Pages | 263-280 |

Number of pages | 18 |

ISBN (Print) | 9781612091303 |

State | Published - 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Advances in Analysis: Problems of Integration*(pp. 263-280). Nova Science Publishers, Inc.

**An integral equation for Feynman's operational calculi.** / Nielsen, Lance.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Analysis: Problems of Integration.*Nova Science Publishers, Inc, pp. 263-280.

}

TY - CHAP

T1 - An integral equation for Feynman's operational calculi

AU - Nielsen, Lance

PY - 2012

Y1 - 2012

N2 - In this paper we develop an integral equation satisfied by Feynman's operational calculi in formalism of B. Jefferies and G. W. Johnson. In particular a "reduced" disentangling is derived and an evolution equation of DeFacio, Johnson, and Lapidus is used to obtain the integral equation. After the integral equation is presented, we show that solutions to the heat and Schrodinger's equation can be obtained from the reduced disentanglingand its integral equation. We also make connections between the Jefferies and Johnson development of the operational calculi and the analytic Feynman integral.

AB - In this paper we develop an integral equation satisfied by Feynman's operational calculi in formalism of B. Jefferies and G. W. Johnson. In particular a "reduced" disentangling is derived and an evolution equation of DeFacio, Johnson, and Lapidus is used to obtain the integral equation. After the integral equation is presented, we show that solutions to the heat and Schrodinger's equation can be obtained from the reduced disentanglingand its integral equation. We also make connections between the Jefferies and Johnson development of the operational calculi and the analytic Feynman integral.

UR - http://www.scopus.com/inward/record.url?scp=84892135552&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892135552&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:84892135552

SN - 9781612091303

SP - 263

EP - 280

BT - Advances in Analysis: Problems of Integration

PB - Nova Science Publishers, Inc

ER -