about Pfadintegral dotCom


co | lo | phon

[Via late Latin colophōn, from Greek kolophōn; ‘summit, finishing touch’]

publication details in books: the details of the title, printer, publisher, and publication date given at the end of a book. Colophons are commonly found in early printed books and in modern private press editions.

Encarta® World English Dictionary

Inspired by the idea of a colophon, I follow the tradition of giving a brief description of the publication and technical details about my ‘modern private digital edition’.

pfadintegral ? what is this ?

Pfadintegrale, or path integrals, were first conceived by Richard Feynman in 1942 as a powerful conceptual and computational tool in quantum physics. The formalism of Feynman path integrals provide an elegant framework for considering problems containing random or stochastic variables. The basic idea of a path integral is the propagation of information in time by an infinite set of infinitesimal time steps and describe the probabilities of different paths a stochastic dynamical system can follow.

The set of all possible paths starting at a certain initial state to a final state and the expectation values of variables depending on those paths are summed over by path integrals (‘sum over histories’). The path integral is also a ‘functional’ in the sense, that the paths themselves are functions dependent on time.

Recently the applications of path integrals is moving out from physics into the realms of practical problems in mathematical finance as well. The main motivation and starting point for introducing path integrals is to enlarge the tool set for studying option pricing applications, which are well known to be highly non-linear random systems. To express the problems in option pricing theory as a Feynman path integral has proven to be a powerful tool allowing for efficient algorithms.

Following Linetzky [1998] or Kleinert [2002] the relevance of path integrals in the field of mathematical finance was first recognized by the theoretical physicist Jan Dash in 1988, who composed two unpublished papers on the subject with the title Path Integrals and Options I and II (available on the web site of Hagen Kleinert).

design ?

All the design of this website grew out of my ideas and layout sketches. The site uses a simple, mainly ‘elastic’ em based two column page layout, which means that the layout should scale with users’ text size. I just like the clean and ‘boxy’ presentation scheme, without too much glossy web2.0-ish stuff.

markup and styling ?

This is my first web site, thus I try to adapt the actual web standards based on the W3C® recommendations right from the start. For my purpose, I chose to mark up the content in XHTML 1.0 Strict and style the content with a separate CSS 2.1 compliant style sheet. As a very good guideline, at least for me, serve the recommendations on microformats about Plain Old Semantic HTML, which encapsulates the best practices of using semantic HTML to author web pages. Highly recommended.

Valid XHTML

Valid CSS

I tried this site with some widespread browsers and it seems to be fine; for that reason I hope, that the content is accessible to any browser. Though, if you have any serious problems using a more or less actual browser, please drop me a line.

After prototyping with plain static HTML pages I pushed my markup to a Content Management System (CMS). The content is managed using MODx, a flexible and highly modular framework, which allows adding and administration of content like a breeze.

what is MODx ?

MODx helps you take control of your online content. An Open Source Content Management Framework, it frees you to build sites exactly how you want and make them 100% yours. Zero restrictions and fast to build. Super-simple templates in HTML/CSS/JS (any lib you want). Registered user systems and a killer community. Welcome to web-building nirvana.

the MODx CMS project

I have nothing to add.

Runs with MODx

Runs with MODx

some more technicalities …

Everything at Pfadintegral dotCom is hand-written and build up from scratch. To accomplish my task I rely heavily on the excellent tool Notepad++ to catalyse the workflow. I like it simply for the reason of the economic value added it has to offer with syntax highlighting, auto-completion and nice indenting capabilities, just to mention a few invaluable features. Of course, there are lots of other tools that come in handy; for a comprehensive list with quite useful applications and if looking for something specific, the Hanselman Ultimate Tools List is the place to look at.

Thank you for your interest !