Functional Integrals Connected With Operator Evolution Equations

Daletskii, Yu. L.

doi:10.1070/rm1962v017n05abeh004121

Cited by 44 publications

(28 citation statements)

References 64 publications

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“…Theorem 1.1, which illustrates its failure, is due to Cameron (1960); see also Daletskii (1961Daletskii ( , 1962 and Truman (1978a). Theorem 1.1, which illustrates its failure, is due to Cameron (1960); see also Daletskii (1961Daletskii ( , 1962 and Truman (1978a).…”

Section: More About Other F-integral Theoriesmentioning

confidence: 98%

Open Quantum Systems and Feynman Integrals

Exner¹

1985

189

186

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All Rights Reserved© 1985 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover I st edition 1985 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the oopyright owner TO MY PARENTSWho taught me to perceive beauty and honour truth

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Section: More About Other F-integral Theoriesmentioning

confidence: 98%

Open Quantum Systems and Feynman Integrals

Exner¹

1985

189

186

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“…However there are different approaches to regularization of path integrals, see [4,23] for recent accounts. It is known that path integrals give fundamental solutions of evolutionary equations [3]. Particularly wave functions (2.4) are solutions to the Schrödinger equa-…”

Section: Preliminaries On Path Integralsmentioning

confidence: 99%

“…* On leaving form the Odessa National University (Ukraine). 3. The falling factorial sequence p n (x) = x(x − 1) · · · (x − n + 1).…”

Section: Introduction To Polynomial Sequences Of Binomial Typementioning

confidence: 99%

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Polynomial Sequences of Binomial Type Path Integrals

Kisil

2002

Annals of Combinatorics

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Polynomial sequences p n (x) of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express p n (x) as a path integral in the "phase space" N × [−π, π]. The Hamiltonian is h(φ) = ∑ ∞ n=0 p n (0)/n! e inφ and it produces a Schrödinger type equation for p n (x). This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an algorithm for parallel quantum computation.

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“…Daletskii [4,5] treated related problems, but did not construct a countably additive path space measure. By the way, it is just in the same way that the Wiener measure was constructed for the heat equation or imaginary-time Schr/Sdinger equation (Nelson [28].…”

Section: 6) V Exp I [P()¢() -mentioning

confidence: 99%