Lance Nielsen

Stability properties of Feynman's operational calculus for exponential functions of noncommuting operators

Stability properties of Feynmans operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.

Feynman's operational calculus and beyond : noncommutativity and time-ordering

1. Introduction 2. Disentangling: Definitions, Properties and Elementary Examples 3. Disentangling via Tensor Products and Ordered Supports 4. Extraction of Multilinear Factors and Iterative Disentangling 5. Auxiliary Operations and Disentangling Algebras 6. Time-Dependent Feynmans Operational Calculus and Evolution Equations 7. Stability Properties of Feynmans Operational Calculi 8. Disentangling via Continuous and Discrete Measures 9. Derivational Derivatives and Feynmans Operational Calculi 10. Spectral Theory for Noncommuting Operators 11. Epilogue: Miscellaneous Topics and Possible Extensions

Effects of absolute continuity in Feynman’s operational calculus

We investigate the effects of having an absolute continuity relation between the time-ordering measures in Feynmans operational calculus. In particular, we obtain some theorems concerning the formation of functions of several noncommuting operators or operator-valued functions under specific absolute continuity assumptions on the time-ordering measures.

Single Peaked Fuzzy Preferences In One-Dimensional Models: Does Black'S Median Voter Theorem Hold?

Blacks Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed on a single-dimensional continuum such that the preferences of all players descend monotonically from their ideal point, then the outcome will be the alternative at the median position. We demonstrate that the Median Voter Theorem holds for fuzzy preferences. Our approach considers the degree to which players prefer options in binary relations.