# Tom Copeland

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 Name Tom Copeland Member for 2 years Seen May 21 at 20:47 Website Location Age
 Apr16 comment Does the derivative of log have a Dirac delta term?@Liviu, anticipating? Check the dates. Dirac was famous for his terseness, originality, and ingenuity, as reflected in his presentation. Apr16 comment Does the derivative of log have a Dirac delta term?@Terry, given the earlier stated answers below, your comment seems at best redundant. Maybe you could expand on it as an answer and provide some new details for those not already familiar with the theory of distributions Apr15 comment Does the derivative of log have a Dirac delta term?Really, weren't the results for the limiting case of the derivative of the log worked out fairly rigorously by Cauchy and Poisson in their work on potential theory long before 20'th century mathematicians put a formal dress on them? Apr15 comment Does the derivative of log have a Dirac delta term?Dirac would have known all these results from electrostatics to corroborate his assertion. Apr15 comment Does the derivative of log have a Dirac delta term?Terry, you're missing a derivative. d/dz log(z)=1/z then look at limits as in the Poisson kernel. Apr15 comment Does the derivative of log have a Dirac delta term?Dirac's bachelor's degree was in electrical engineering at a British university, so I'm sure he was familiar with and influenced by Heaviside's style of mathematics. Apr15 comment Does the derivative of log have a Dirac delta term?For those who may be a little confused about the absolute value sign, just switch to polar coordinates and restrict to the real line. Apr15 comment Does the derivative of log have a Dirac delta term?I'm sure Dirac was thinking that ln(x)=ln|x|+i H(-x)π, where H(x) is the Heavside step function. Apr10 awarded ● Popular Question Jan16 comment Motivation of Virasoro algebra@Muon : Actually, you mean $z^{n+1}$. I'll expand on my comment later. I think a good answer to your questions would involve combining ideas in Khesin and Wendt's The Geometry of Infinite-Dimensional Groups, Ovsienko and Tabachnikov's Projective Differential Geometry Old and New, and the book I cited earlier in a tight narrative, but that's beyond me at the moment. Jan12 awarded ● Yearling Jan9 comment History of the Sampling Theorem@Eremenko : the paper you cite in the edit is precisely the one in my answer. Why the repetition? Luke in the cited paper states, "The first scientist to formulate the sampling theorem precisely and apply it to problems of communication engineering is probably V. A. Kotelnikov." (1933) Jan9 comment Hopf Algebra for a physicistFor a physicist with an interest in QED perhaps a good place to start is Sec. 3.3 Fusion, Splitting, and Hopf Algebras in E. Zeidler's book Quantum Field Theory II Quantum Electrodynamics. Jan7 comment History of the Sampling TheoremDon't confuse the son J. M. (1929, and later in his book in 1935) with the father E.T. (1915) who is actually given the majority of the credit for a bandwidth analysis. (I guess you see what you look for.) If you're concerned about accreditation to Russians, you might want to confirm (or not) the chronology at the website linked to in my answer which notes Kotelnikov (1930), as well as other nationalities (Ogura, 1920). Dec27 comment Motivation of Virasoro algebraAs a first step at understanding the relations, I always recall that $exp(-c \cdot z^2d/dz)f(z)=exp[c \cdot d/d(1/z)]f(1/(1/z))=f(1/(c+1/z))=f(z/(cz+1)),$ a special conformal transformation. Note $zd/dz=d/d(ln(z))$ for the dilatation. Dec27 comment Motivation of Virasoro algebraTry Ch. 9: Conformal Invariance Sec. 9.1: Energy momentum tensor-Virasoro algebra of the book Statistical Field Theory Vol. 2 by Itzykson and Drouffe. Maybe you could work around pg. 514 on translations, complex dilatations, and special conformal transformations related to $d/dz, zd/dz,$ and $z^2d/dz$.The central charge is discussed in the next sub-section from a physical and mathematical perspective. Dec26 revised The Dedekind Eta Function in PhysicsFinal update Dec26 revised The Dedekind Eta Function in Physicsdeleted 3 characters in body Dec26 revised The Dedekind Eta Function in PhysicsMore specifics Dec24 revised The Dedekind Eta Function in PhysicsDeleted remark confusing Dirichlet eta with Dedekind Dec24 revised The Dedekind Eta Function in PhysicsSpecifics Dec24 revised The Dedekind Eta Function in PhysicsNew info Dec21 comment A Dedekind Eta trajectory / horocyclic flow (Reference request)I wonder if the first curve could be lifted off the plane onto a double torus with one torus nested inside the other but sharing its circle of max radius with that of the other torus. Dec20 comment A Dedekind Eta trajectory / horocyclic flow (Reference request)We're essentially looking at solns. around $z=0$ and infinity of the eigenfunction eqn. $\exp(t\cdot z^2 \frac{\partial }{\partial z}) f(z)=f[z/(-tz+1)]=\epsilon(t) f(z)$ for some $t$. The simplest case being $f(z)=\exp(-\lambda/z)$. Dec20 comment A Dedekind Eta trajectory / horocyclic flow (Reference request)Hi Dan--the results above depend on $\eta$ being a modular form. I don't see how to get the necessary periodicity with any polynomial under shear transformations. Scan my notes on Infinigens at my little "arxiv website" for details. Dec20 revised A Dedekind Eta trajectory / horocyclic flow (Reference request)Extra info Dec19 revised A Dedekind Eta trajectory / horocyclic flow (Reference request)Refined discussion Dec17 revised A Dedekind Eta trajectory / horocyclic flow (Reference request)Added another figure Dec17 revised A Dedekind Eta trajectory / horocyclic flow (Reference request)Better graphics Dec17 asked A Dedekind Eta trajectory / horocyclic flow (Reference request) Dec11 awarded ● Disciplined Dec7 revised The Dedekind Eta Function in Physicsadded 463 characters in body Dec5 comment Conjugation: The nature of the beast--spawn, perspectives, broadest formulationQuandles and racks would have been a good example of an answer. Dec3 revised The Dedekind Eta Function in Physicsdeleted 1 characters in body Dec3 revised The Dedekind Eta Function in Physicsadded 402 characters in body Dec3 revised The Dedekind Eta Function in Physicsadded link, fixed typos Dec3 asked The Dedekind Eta Function in Physics Nov29 comment Geometric / physical / probabilistic interpretations of Riemann zeta(n>1)?See also Itzykson and Zuber's "Matrix Integration and Combinatorics of the Modular Group" lpthe.jussieu.fr/~zuber/MesPapiers/iz_CMP90.pdf Nov28 awarded ● Good Question Nov27 revised Are there other nice math books close to the style of Tristan Needham?added 179 characters in body