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Title: Lectures on differential equations for Feynman integrals

Publication Date:
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
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Grant/Contract Number:
Resource Type:
Journal Article: Published Article
Journal Name:
Journal of Physics. A, Mathematical and Theoretical
Additional Journal Information:
Journal Volume: 48; Journal Issue: 15; Related Information: CHORUS Timestamp: 2017-06-23 04:00:04; Journal ID: ISSN 1751-8113
IOP Publishing
Country of Publication:
United Kingdom

Citation Formats

Henn, Johannes M. Lectures on differential equations for Feynman integrals. United Kingdom: N. p., 2015. Web. doi:10.1088/1751-8113/48/15/153001.
Henn, Johannes M. Lectures on differential equations for Feynman integrals. United Kingdom. doi:10.1088/1751-8113/48/15/153001.
Henn, Johannes M. 2015. "Lectures on differential equations for Feynman integrals". United Kingdom. doi:10.1088/1751-8113/48/15/153001.
title = {Lectures on differential equations for Feynman integrals},
author = {Henn, Johannes M.},
abstractNote = {},
doi = {10.1088/1751-8113/48/15/153001},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 15,
volume = 48,
place = {United Kingdom},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1088/1751-8113/48/15/153001

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Cited by: 46works
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  • It is shown that every Feynman integral can be interpreted as a Green function of some linear differential operator with constant coefficients. This definition is equivalent to the usual one but needs no regularization and application of the [ital R] operation. It is argued that the presented formalism is convenient for practical calculations of Feynman integrals.
  • The theme of this paper is the study of the symmetry properties of some differential equations of dynamics, and of the construction of first integrals. For the time-dependent harmonic oscillator the Lewis invariant provides a quadratic function which is a constant of motion. Different derivatives are considered with a view to assigning some physical meaning to the invariant and to the function rho(t) in terms of which the invariant is expressed. Lie's theory of differential equations, which until recently has been sadly neglected in comparison with his other pioneering works, is applied to consider groups of point transformations which leavemore » invariant the equations of motion. For the time-dependent oscillator, an eight-parameter Lie group is obtained. A five-parameter Noether sub-group leaves also the action function invariant. Some results concerning the symmetries of the Kepler problem are also reported. Dynamical symmetries, not covered by point transformations, are briefly discussed.« less