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Provided by David Delphenich  Curriculum Vita Conferring with a distinguished
colleague: Professeur Goofé of
l’Institut des Hautes Études
Email: feedback@neoclassicalphysics.info Félins (IHEF, RIP)
Light reading:
If you have ever noticed how many times the predictions of futurists in the past have been wildly off the mark, while sometimes a few of them also managed to say things that really came to pass, you might find my printondemand paperback book to be entertaining. It's called Probing the Future: the art and science of prediction, and it consists of two parts: In the first part, the psychological need to predict the future is examined, along with a historical timeline of mankind's attempts to predict the future, both scientific and purely imaginative. In the second part, the approach of general systems theory is taken in order to analyze the main reasons that the future states of complex dynamical systems can be so hard to predict, and numerous examples are given of such systems in nature, psychology, economics, and other applications.
The book is available at Booklocker.com for $19.95 plus shipping and handling.
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colleague: Professeur Goofé of
l’Institut des Hautes Études
Email: feedback@neoclassicalphysics.info Félins (IHEF, RIP)
Light reading:
If you have ever noticed how many times the predictions of futurists in the past have been wildly off the mark, while sometimes a few of them also managed to say things that really came to pass, you might find my printondemand paperback book to be entertaining. It's called Probing the Future: the art and science of prediction, and it consists of two parts: In the first part, the psychological need to predict the future is examined, along with a historical timeline of mankind's attempts to predict the future, both scientific and purely imaginative. In the second part, the approach of general systems theory is taken in order to analyze the main reasons that the future states of complex dynamical systems can be so hard to predict, and numerous examples are given of such systems in nature, psychology, economics, and other applications.
The book is available at Booklocker.com for $19.95 plus shipping and handling.
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Latest updates
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Since new files are being added to this site continually, if you would like to be notified by email whenever the site has been updated, leave an email at feedback@neoclassicalphysics.info with the word "subscribe" in the subject line. If you no longer wish to be notified, put "unsubscribe" in the subject line. (No salesman will call!)
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(5/25/19): Two papers by Engel on Pfaff systems (Analysis):
F. Engel, "On the invariant theory of systems of Pfaff equations," Ber. Verh. Sachs. Ges. Wiss. 41 (1889), 157176.
F. Engel, "On the invariant theory of systems of Pfaff equations (second communication)," Ber. Verh. Sachs. Ges. Wiss. 42 (1890), 192207.
(6/1/19): More papers on Pfaff and Monge equations (Analysis):
J.A. Serret, "On the integration of the equation dx2 + dy2 + dz2 = ds2," J. math. pures appl. 13 (1848), 353368.
A. Mayer, "On unrestricted integrable systems of linear total differential equations and the simultaneous integration of linear partial differential equations," Math. Ann. 5 (1872), 448470.
E. von Weber, "On the invariant theory of systems of PFAFF equations," Ber. Verh. Kon. Ges. Wiss. 50 (1898), 207229.
(6/8/19): A paper on least constraint and my latest upload to arXiv.org (Theoretical mechanics):
E. Schering, "HamiltonJacobi theory of forces whose measure depends upon the motion of the body," Abh. Kön. Ges. Wiss. 18 (1873), 354.
D. H. Delphenich, "The role of pseudohypersurfaces in nonholonomic motion," arXiv:1906.00714.
(6/15/19): A book by von Lilienthal on the geometry of congruences (Geometry):
R. von Lilienthal, Foundations of a theory of curvature of families of curves, Teubner, Leipzig, 1896.
(6/23/19): More papers on anholonomic manifolds and nonholonomic constraints (Geometry, Theoretical mechanics):
I. Tzenoff, "On the general equations of motion of nonholonomic systems," J. Math. pures appl. (8) 3 (1920), 245263.
I. Tzenoff, "On the motion of nonholonomic systems," J. Math. pures appl. 9 (1925), 193207.
Z. Horak, "On the curvature of nonholonomic manifolds," C. R. Acad. Sci. Paris 187 (1928), 12731276.
G. Vranceanu, "Geometric study of anholonomic systems," Ann. di Mat. pure ed appl. (4) 6 (192829), 943.
A. Wundheiler, "On the variational equations for affine geodetic lines and nonholonomic, nonconservative dynamical systems," Prace Mat. Fiz. (1931), 129147.
Z. Horak, "On the absolute equations of motion," Casopis pro pestovani a fysiky 64 (1935), 229230.
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The natural philosophy of neoclassical physics
What I am calling “neoclassical” physics refers to the constellation of research topics that lie at the interface between classical physics and quantum physics. This does not always represent the physical phenomena that are left when one takes the classical limit as Planck’s constant goes to zero. Indeed, some of the topics include the tensor form of the Schrödinger and Dirac equations and the association of physical observables with the quantum wave function. Mostly, one tries to reconcile the “stronglyworded hints” that come from the effective field theories with the possible improvements one might incorporate into the fundamental model for the electromagnetic vacuum state in order to extend from classical electromagnetism to quantum electromagnetism.
One of the subtle issues that asserts itself in quantum physics is the integrability of the work functional, such as whether the basic flaw in the Dirac sea model of the quantum electromagnetic vacuum state is in assuming that it consists of total potential energy states for the fields of positrons, when those states have infinite energy. Since, as Heisenberg explained, “it isn’t the infinities that are physically meaningful, only the difference between them,” this suggests that perhaps one should not assume that the work done going from one state to another is actually conservative, rather than something more “thermodynamic” going on with the energy of quantum fields. If one puts the force 1form that defines the kernel of the work functional into normal form, in the Pfaffian sense, as a sum of an exact form and various inexact contributions then perhaps those obstructions to the integrability of the force 1form might represent “quantum corrections” to the classical expression – i.e., the exact part.
This program of research also entails gaining more intuition about how the modern geometrical and topological methods in mathematical physics apply at the elementary level in empirically reachable phenomena. For instance, although topologychanging process are often first introduced in field theory as a Planck scale process, nevertheless, the concept is much more commonplace in nature than just the early Big Bang. For instance, one can see topologychanging processes at work in the growth of a tree, the formation of soap bubbles and smoke rings, and the nucleation of bubbles in boiling water. Ideally, one hopes that the laws of nature at their most fundamental level are truly universal, which is the spirit of the various principles of relativity, and the only hope for astronomy and cosmology, and that the most powerful tool in the theoretical toolbox is reasoning by analogy.
Some of the topics represented in the research that papers that I have provided in PDF form for download are:
1. The nonstatistical interpretation of the quantum wave function, such as the hydrodynamic interpretation of Madelung, Schönberg, Takabasi, and Halbwachs, and the electrical interpretation of Schrödinger, Pauli, and Weisskopf.
2. The papers in quantum electrodynamics that followed the publication of Dirac’s seminal paper on the theory of the electron.
3. Quantum enhancements to the classical electron model of Abraham, Lorentz, and Poincaré that would take into account the magnetic moment of the electron, its wavelike nature, and the existence of antimatter and vacuum polarization.
4. Extensions of classical electromagnetism to include nonlinear superposition, a more fundamental model of the electromagnetic vacuum that would include vacuum polarization at high field strengths, and the possibility that the electromagnetic structure of spacetime is more fundamental than the metric structure, since the spacetime metric follows from the dispersion law for the propagation of electromagnetic waves.
5. Alternative ways of formulating mechanics itself that anticipate the extension to a mechanics of general waves that includes quantum waves, as well as classical ones. In particular, projective geometry plays a deeper role in the mechanics of points, rigid bodies – which include rigid structures, as well as rigid solids, – continua, and waves than is often appreciated nowadays.
6. In particular, the formulation of any mechanical theory as something that is based in the action of Lie groups (if not pseudogroups and groupoids) of transformations on the configuration space of the model.
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Research papers
The papers available for download include my own research, as well as my English translations of various classical books, articles, and pamphlets that originally appeared in French, German, and Italian. Please feel free to inform me of any corrections that need to be made or any suggestions you might have about other translations.
MATHEMATICS:
Algebras – Frobenius, quaternions (real, dual, complex)
Topology  Homology, foliations, singularities, parallelizability
Geometry – projective, line, differential geometry, Lie pseudogroups and groupoids
Analysis – Pfaff problem, geodesic fields, calculus of variations, contact transformations
PHYSICS:
Spacetime structure – geometry and topology, unified field theories
Theoretical mechanics – points, rigid bodies, structures, continua
Electromagnetism – classical and quantum, premetric electromagnetism
Wave theory – classical and quantum waves, contact transformations, geometrical optics
Thermodynamics – Papers by Helmholtz, Carathéodory, de Broglie, and Lippmann, and a book by de Broglie
NATURAL SYSTEMS:
General systems theory  Papers by Verhulst and Volterra on the dynamics of natural systems
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Online resources
bookfinder.com  A worldwide search engine for online used book dealers
Worldcat.org  A good place to find where in the world one might find a copy of any given book or journal
books.google.com  A good source for free downloads of many classical references that are now in the public domain,
or often brief glimpses of the references that are still protected by copyright
archive.org  Another good source for books and journals that are in the public domain now
arXiv.org  (Not to be confused with archive.org) The main artery of announcement for physics research
papers
Digizeitschriften.de  A source of free downloads of mostly German journals
Gallica.bnf.fr  Somewhat like Digizeitschriften, but for mostly French journals
Cartan’s Corner  A website devoted to Eli Cartan and the application of his ideas to physics provided by Bob Kiehn
Friedrich Hehl  A colleague who has encouraged and inspired much of my research
Yuriy Krasnov  A colleague for whom I once edited a book on the dynamics of quantum vortices, which is available
for download (now deceased).
J.F. Pommaret  A mathematician and civil engineer who has examined the application of Spencer cohomology to
Cosserat media in great detail