Lance W . Nielsen, PhD

## Professor

### Contact

College of Arts and Sciences

Mathematics

HLSB - Hixson Lied Science Building

# Lance W . Nielsen, PhD

## Professor

*Feynman's operational calculus*, an area of mathematics closely related to quantum mechanics and quantum electrodynamics which was originated by R. P. Feynman in approximately 1950.

### Teaching Interests

- Feynman's operational calculus

### Research Focus

Feynman's operational calculus, complex dimensions and fractal strings.### Department

Mathematics

### Position

Professor

### Books

- Blending Instantaneous and Continuous Phenomena in Feynman’s Operational Calculus with G. W. Johnson, in “Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002) Proceedings of the Mathematical Legacy of R. P. Feynman”, World Scientific, Sept. 2004.
**Oxford University Press**

Noncommutativity and Time-Ordering: Feynman’s Operational Calculus and Beyond, with Michel Lapidus and G. W. Johnson, published by Oxford University Press, in print September 2015.

### Articles

**Integral Equations and Operator Theory**

Lance Nielsen, The abstract approach to Feynman's operational calculus using arbitrary time-ordering measures is developed using two approaches to addressing the combinatorial complexities which arise. An evolution equation is established for the second of the two approaches and examples are considered.

94, Issue 2, Article Number 15 2022**New York Journal of Mathematics**

Nielsen, Lance A distributional approach to Feynman's operational calculus

20, p. 377-398 2014**New York Journal of Mathematics**

A Distributional Approach to Feynman’s Operational Calculus, New York J. of Math. 20 (2014), 1-22.

2014, p. 1-22 2014**Journal of Doctoral Nursing Practice**

Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent Setting, Acta Appl. Math., 2014, in press. DOI 10.1007/s10440-014-9957-1.

2014 2014**Journal of Fuzzy Mathematics**

Fuzzy Cores in Spatial Models, J. of Fuzzy Mathematics, Vol. 21, No. 4, 2013.

21, 4 2013**Mathematical Physics, Analysis and Geometry**

Nielsen, Lance Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman's Operational Calculi

14, p. 279-294 2011**Mathematical Physics, Analysis and Geometry**

Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi, Math. Phys. Anal. Geom. 14 (2011), 279-294.

14, 2014 2011**Acta Applicandae Mathematicae**

Nielsen, Lance Feynman's Operational Calculi: Disentangling Away from the Origin

110, p. 409-429 2010**Critical Review**

Clark, T. D., Mordeson, J. N., Nielsen, L., Wierman, M. J. Fuzzy geometry: applied to comparative politics

2, p. 1-12 2008**Mathematical Physics, Analysis and Geometry**

Nielsen, L. Weak convergence and vector-valued functions: Improving the stability theory of feynman's operational calculi

10, p. 271-295 2007**Mathematical Physics, Analysis and Geometry**

Jefferies, B., Johnson, G. W., Nielsen, L. Feynman's operational calculi: Spectral theory for noncommuting self-adjoint operators

10, p. 65-80 2007**Acta Applicandae Mathematicae**

Nielsen, L. Stability properties for feynman's operational calculus in the combined continuous/discrete setting

88, p. 47-79 2005**Rocky Mountain Journal of Mathematics**

Nielsen, L. Time dependent stability for Feynman's operational calculus

35, p. 1347-1368 2005**Journal of the Korean Mathematical Society**

Feynman’s Operational Calculi for Time Dependent Noncommuting Operators, with Brian Jefferies and G. W. Johnson, J. Korean Math. Soc. 38 (2001), 193 – 226

38, 2001, p. 193-226**Conference Proceedings, Canadian Mathematical Society**

A Stability Theorem for Feynman’s Operational Calculus, with G. W. Johnson, Conference Proc., Canadian Mathematical Society, 29 (2000), 351 – 365

29, 2000, p. 351-365**Proceedings of the American Mathematical Society**

Effects of Absolute Continuity in Feynman’s Operational Calculus, Proc. Amer. Math. Soc. 131 (2003), 781-791

131, 2003, p. 781-791**Acta Applicandae Mathematicae**

Stability Properties of Feynman’s Operational Calculus for Exponential Functions of Noncommuting Operators, Acta Applicandae Mathematicae 74, 2002, 265 – 292

74, 2002, p. 265-292**Rocky Mountain Journal of Mathematics**

Time Dependent Stability for Feynman’s Operational Calculus, Rocky Mountain Journal of Mathematics 35 no. 4 (2005), 1347 - 1368

4, 2005, p. 1347-1368**Acta Applicandae Mathematicae**

Stability Properties for Feynman’s Operational Calculus in the Combined Continuous/Discrete Setting, Acta Applicandae Mathematicae 88 (2005), 47 – 79.

88, 2005, p. 47-79**Mathematical Physics, Analysis and Geometry**

Feynman’s Operational Calculi: Spectral Theory for Noncommuting Self – Adjoint Operators, with B. Jefferies and G. W. Johnson, Mathematical Physics, Analysis, and Geometry, 10 (2007), 65 - 80

10, 2007, p. 65-80**Mathematical Physics, Analysis and Geometry**

Weak Convergence and Vector-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi, Mathematical Physics, Analysis, and Geometry, 10 (2007), 271 - 295.

10, 2007, p. 271-295**Integration: Mathematical Theory and Applications**

An Integral Equation for Feynman’s Operational Calculus, Integration: Mathematical Theory and Applications, Volume 1, Number 1, 2008, pp. 49 - 66.

1, 2008, p. 49-66**Acta Applicandae Mathematicae**

Feynman’s Operational Calculi: Disentangling Away from the Origin, Acta Applicandae Mathematicae ,110 (2010), 409-429.

110, 2010, p. 409-429**New York Journal of Mathematics**

á Feynman’s Operational Calculus : Using Cauchy’s Integral Formula, New York J. of Math. (16) 2010, 1 - 26.

16, 2010, p. 1-26**Mathematical Physics, Analysis and Geometry**

Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi, Math. Phys. Anal. Geom. 14 (2011), 279-294.

14, 2011, p. 279-294**New York Journal of Mathematics**

A Distributional Approach to Feynman’s Operational Calculus, New York J. of Math. 20 (2014), 1-22.

20, 2014, p. 1-22**Acta Applicandae Mathematicae**

Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent Setting, Acta Appl. Math., 138 (2015), 59-79.

138, 2015, p. 59-79**Acta Applicandae Mathematicae**

Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time-Dependent Setting, submitted for publication, July 30, 2015.

152 (2017), p. 1-31**Integral Equations and Operator Theory****Combining Continuous and Discrete Phenomena for Feynman’s Operational Calculus in the Presence of a (C0) Semigroup and Feynman-Kac Formulas with Lebesgue-Stieltjes Measures**

Nielsen, L. Integr. Equ. Oper. Theory (2018) 90: 12. https://doi.org/10.1007/s00020-018-2428-8**New York Journal of Mathematics**

"Two Approaches to the Use of Unbounded Operators in Feynman's Operational Calculus"

### Editing and Reviews

- Analytic Tools for Feynman Integrals, by Vladimir Smirnov, Springer Tracts in Modern Physics 250, Springer, 2012. (Monograph) 2012

### Presentations

- Invited lecture at the South Dakota State University department of mathematics seminar. Title: "Essential Ideas and Properties of Feynman's Operational Calculus." 2018
- Presented the invited talk "Feynman's Operational Calculus: Background and Esential Properties" at the spring 2017 Nebraska-Iowa Functional Analysis Seminar at Creighton University. 2017
- Presented the talk: "Combining Continuous and Discrete Phenomena in Feynman's Operational Calcuus in the Presence of a (C_0) Semigroup: Feynman-Kac Formulas with Lebesgue-Stieltjes Measures" at the Joint Meetings of the AMS in Atlanta, GA. 2017
- Presented the talk "An Evolution Equation for Feynman's Operational Calculus in the Combined Continuous/Discrete Setting" at the Joint Meetings of the AMS in Seattle, WA, Jan. 2016. 2016
- Presented the invited talk “Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent Setting” during the special session “AMS Special Session on Advances in Analysis and PDEs” at the Joint Meetings of the American Mathematical Society in Baltimore, Jan. 2014. 2014
- Presented the contributed talk “Feynman’s Operational Calculus: Using Cauchy’s Integral Formula” at the Joint Meetings of the AMS, Boston, January 2012. 2012
- Presented 'Stability Properties for Feynman's Operational Calculus' at the International Conference on Feynman Integrals and Related Topics. 1999
- Eight lectures on on-going research at the Functional Integration Seminar at UNL in the fall of 2004
- Presented 6 lectures on current research at the Functional Integration Seminar at UNL during the Fall of 2000.
- Presented 'Effects of Absolute Continuity in Feynman's Operational Calculus' at the Joint Meetings of the AMS, January 2001.
- Presented 6 lectures on current research at the Functional Integration Seminar at UNL in the Spring of 2001
- Presented 8 lectures on current research at the Functional Integration Seminar during the Fall of 2002.
- Presented 5 lectures on current research at the Functional Integration Seminar at UNL in Spring 2003.
- Presented 'Blending Instantaneous and Continuous Phenomena in Feynman's Operational Calclus' at the Joint Meetings of the AMS, Jan. 2003
- Invited Lecture - 'A Survey of Feynman's Operational Calculus' at the Nebraska Iowa Functional Analysis Seminar, April 2003.
- Presented 8 lectures on current research at the Functional Integration Seminar at UNL in Fall 2004
- Presented 'An Integral Equation for Feynman's Operational Calculus' at the Joint Meetings of the AMS, Jan. 2005.
- Presented 5 lectures on current research at the Functional Integration Seminar at UNL, spring 2005.
- Presented 5 lectures on current research at the Functional Integration Seminar at UNL in Spring 2006.
- Presented 'An Integral Equation for Feynman's Operational Calculus' at 'The Feynman Integral and Related Topics in Mathematics and Physics' at UNL in 2006.
- Presented 6 lectures at the Functional Integration Seminar, Spring 2007.
- Presented 5 lectures at the Functional Integration Seminar at UNL in Fall 2007.
- Presented 'Weak Convergence and Vector-Valued Functions: Improving the Stability Theory of Feynman's Operational Calculus' at the Joint Meetings of the AMS, Jan. 2008
- Presented 4 lectures on current research at the Functional Integration Seminar at UNL, Fall 2008.
- Presented 'Feynman's Operational Calculus Beyond an Introduction' at the University of California, Riverside, March 2009.
- Presented the invited lecture “Feynman’s Operational Calculi : Background and a Survey of Current Research” at the Nebraska - Iowa Functional Analysis Seminar in Des Moines, IA
- Presented the invited talk “An Integral Equation for Feynman’s Operational Calculi” at “The 10th International Conference on Path Integrals” held at Howard University, Washington, D.C.
- Presented three lectures at the functional integration seminar at the University of Nebraska, Lincoln, spring 2010.
- Presented two lectures at the functional integration seminar at the University of Nebraska, Lincoln, fall 2010.
- Presented two lectures at the functional integration seminar at the University of Nebrask, Lincoln, spring 2011.
- Presented the invited talk “Feynman’s Operational Calculus: Background and a Survey of Current Research” at the University of Nebraska, Omaha, April 22, 2011
- Presented three lectures at the functional integration seminar at the University of Nebraska, Lincoln, fall 2011.
- Presented three lectures at the functional integration seminar at the University of Nebraska, Lincoln, spring 2012.
- Presented three lectures at the functional integration seminar at the University of Nebraska, Lincoln, fall 2012.
- Presented the contributed talk “Feynman’s Operational Calculus: Using Cauchy’s Integral Formula” at the Joint Meetings of the AMS, Boston, January 2012.
- Presented the invited talk “Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent Setting” during the special session “AMS Special Session on Advances in Analysis and PDEs” at the Joint Meetings of the American Mathematical Society in Baltimore, Jan. 2014.
- Presented the talk: “Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent and the Time-Dependent Settings” at the Joint Mathematics Meetings, Jan. 2015, in San Antonio.
- Presented the talk: “An Evolution Equation for Feynman’s Operational Calculus in the Combined Continuous/Discrete Setting” at the Joint Mathematics Meetings, Jan. 2016, in Seattle, WA