A functional integral with respect to a countably additive measure representing a solution of the Dirac equation

DOI10.1090/S0077-1554-05-00150-0zbMath1271.81072OpenAlexW1891470660MaRDI QIDQ2841118

N. N. Shamarov

Publication date: 24 July 2013

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0077-1554-05-00150-0

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Vector-valued measures and integration (46G10) Applications of functional analysis to differential and integral equations (46N20) Set functions, measures and integrals with values in abstract spaces (28B99) Green's functions for elliptic equations (35J08)

Related Items (4)

Maslov-Poisson measure and Feynman formulas for the solution of the Dirac equation ⋮ New method for constructing Chernoff functions ⋮ Equivalence of two definitions of a chronological integral ⋮ DISCONTINUITY OF FOURIER TRANSFORMS OF POISSONIAN TYPE COUNTABLY ADDITIVE MEASURES

Cites Work

• Path integral for some systems of partial differential equations
• Feynman's formula in phase space for systems of pseudodifferential equations with analytic symbols
• Matrix-valued cylindrical measures of Markov type and their Fourier transforms
• Schrödinger-Belavkin equations and associated Kolmogorov and Lindblad equations
• A construction of the fundamental solution for the relativistic wave equation. I
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