Mike Vaughn's Home Page
Professor of Physics|
Boston, MA 02115
Tel: (617) 373-2954
E-mail: m.vaughn at neu dot edu
Ph. D., Purdue University, 1960
Field of Specialization: Elementary particle theory
After many years, I have finished a graduate level textbook and reference work on mathematical physics with the mundane title
"Introduction to Mathematical Physics". The important new feature of
this book is the introduction of differential forms and other
geometrical concepts early on (in chapter 3). There are also
introductions to nonlinear problems, and to group theory, and
a reduced emphasis on the special functions that arise in the
solution of Laplace's equation and its relatives.
The book is published by
The table of contents and a complete chapter 1 can be downloaded from
the Wiley web site. Also the index, if you follow the link to the online version of the book.
You can also read much of the book online through Google(R). If you Google(R) on
"Introduction to Mathematical Physics" Vaughn
an early link will be to the Google books site. The book is also available from the usual online booksellers.
A collection of problem solutions (not complete) for instructors
who adopt the book for a course is available from the publisher.
There is a page of errata for the book. Please e-mail me questions, comments, corrections and any other feedback.
In the Fall 2008 semester, I am teaching
In the Spring 2008 semester, I taught
-- Classical Mechanics and Mathematical Physics (first-year physics graduate students)
-- Computational Physics (second-year physics graduate students)
In the Fall 2007 Semester, I taught
-- Nuclear and Particle Physics (upperclass science majors)
The links above will take you to the respective course home pages.
-- Introduction to Astronomy (undergraduate science elective)
-- Electromagnetic Theory (first-year physics graduate students)
Beyond completing the mathematical physics book noted above, I have
a number of research interests:
PT-symmetry in quantum mechanics
About a year ago, Carl Bender gave a marvelous talk at Northeastern
describing a number of examples in which ostensibly non-Hermitian
operators have purely real spectra. In these examples, it is possible
to define a linear operator P (analogous to parity) and an antilinear operator T (analogous to time reversal), such that the Hamiltonian
is invariant under the product PT, though not under either of them alone. There are now many people working on trying to find other
examples with PT-symmetry, and perhaps finding new physical applications of these models. I will expand this section in due course.
gauge dependence of the electron propagator in QED
Some colleagues recently had the clever idea of trying to measure the
exponent of the mass-shell singularity of the electron propagator,
since it has been known since the mid-1950s that this singularity is
not a simple pole. However, it is also well-known that the exponent
of the singularity is actually gauge-dependent, so it is not a
measurable quantity. I have written a short note to explain this, using dimensional regularization and mass-shell subtraction in a general $R_\xi$ gauge
(the textbook calculations I have seen of the propagator that use dimensional regularization are in Feynman gauge).
This note will not be published, since the result is not new. However, it may have some pedagogical value to illustrate the power of dimensional regularization to eliminate possible infrared singularities that sometimes appear when introducing a small photon mass and
later taking it to zero.
higher symmetries in condensed matter systems
In the late 1990s, I worked with Bob Markiewicz in studying the role of higher symmetries in condensed matter physics, especially in the theory of the cuprate high $T_c$ superconductors and other quasi-two-dimensional condensed matter systems.
renormalization group and unified gauge theories
This section is under construction.
- Michael T. Vaughn, Introduction to Mathematical Physics, Wiley-VCH (2007).
- M.E. Machacek and M.T. Vaughn, "Two-Loop Renormalization Group Equations in a General Quantum Field Theory I. Wave Function Renormalization", Nucl. Phys. B222, 83 (1983); "... II. Yukawa Couplings", ibid. B236, 221 (1984); "... III. Scalar Quartic Couplings", ibid. B249, 83 (1985).
- R.S. Markiewicz and M.T. Vaughn, "Stripes, pseudogaps, and
SO(6) in the cuprate superconductors", J. Phys. Chem. Sol. 59, 1737
- R.S. Markiewicz and M.T. Vaughn, "Classification of the Van Hove Scenario as
an SO(8) Spectrum Generating Algebra", Phys. Rev. B57, 14052 (1998)
- R.S. Markiewicz and M.T. Vaughn, "Higher Symmetries in Condensed Matter
Physics", in "Particles, Strings and Cosmology -- PASCOS98", P. Nath (ed.) ,
World Scientific (Singapore, 1999) (cond-mat/9809119).
This is a work under construction. If you are missing something, please send me e-mail.
last update 8 September 2008
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