[ Physics Department ] [ Institute of Theoretical Physics ] [ Elementary Particle Theory/Mathematical physics group ]


Bengt E W  Nilsson

Head of the Mathematical Physics Group at the Institute of Fundamental Physics
Chalmers University
of Technology

Work address:


Institute of Fundamental Physics
Chalmers University
of Technology
S-412 96 Göteborg

email: tfebn@fy.chalmers.se
tel: +46-31-7723160
fax: +46-31-7723204


Home address:

Körsbärsvägen 12
S-435 43 Pixbo

tel: +46-31-881547




Newtonian mechanics and electromagnetism as formulated by Maxwell in 1864 are perhaps the two prime examples of unifying theories, that is theories that explain large numbers of phenomena using just a few basic assumptions and laws. In the twentieth century the ideas of unification was further implemented with tremendous success in special and general relativity, as well as in the Nobel prize winning work of Glashow, Salam, and Weinberg on the electroweak interactions relating within a common framework all electromagnetic and weak (eg all radioactive decays) phenomena.

The electroweak theory and the theory of strong interactions (forces acting between the constituents of protons etc, the quarks) owe their success to the fact that they work nicely as quantum theories. Quantum mechanics is the most profound aspect of our understanding of nature in that it provides a framework for how to approach phenomena at atomic scales or smaller. All theories purporting to explain microscopic phenomena must adhere to the rules of quantum mechanics. Quantum electrodynamics (QED), as well as the quantum theories for weak and strong nuclear interactions are examples of theories that work extremely well at these small scales. In particular, this is true for QED whose agreement with experiments is better than for any other theory known today.

The enigma of twentieth century physics has for decades been the clash between quantum mechanics and general relativy, that is Einstein's theory of gravity. Seemingly unsurmountable problems appear as soon as one asks questions at the Planck scale (10^(-35) meter), or in the vicinity of black holes.

The most likely cure for these problems is the revision of Einstein's theory that is built into the theory of superstrings. The basic idea is that when approaching the Planck scale one discovers that the fundamental point like building blocks used in ordinary quantum field theories are actually different vibrational modes of an extended object, a string. String theory has many interesting features; it unifies in one single four dimensional quantum theory all known forces and elementary particles, and in the process reduces the number of parameters that need to be determined by experiments from between 20 and 30 (assuming massive neutrinos) to one, not counting Planck's constant and the velocity of light.

The mathematically new structures that emerge from the string has also made an impact in pure mathematics. New connections between different mathematical subdisciplines and novel approaches to computing various quantities in for instance topology has generated a new era of close interactions between physicists and mathematicians. The common denominator in this context is the recent developments in quantum field theory triggered by the string.




Using string theory we hope to answer fundamental questions like:

Why is spacetime four dimensional and what is the structure of it at the Planck scale? Why are there four fundamental forces and what is the reason for the very peculiar spectrum of particles building up matter? What is mass and is there more than four dimensions? How and why did the universe start?

The mathematical physics/elementary particle groups work on problems related to the mathematical formulation and physical interpretation of the string. Using infinite dimensional Lie algebras, conformal field theory, supergravity, Kaluza-Klein techniques, membranes and other higher dimensional extended objects, knot theory, the connection between quantum field theory and topology and differential geometry all sorts of fundamental questions about Nature may be addressed. Some of these techniques are studied also for the fact that they find applications in a much wider context, even outside particle physics and pure mathematics, for instance in condensed matter. To date the best example is perhaps the importance of conformal field theory in the understanding of phase transitions and critical phenomena in condensed matter, polymers etc. In the future we will probably find more applications outside physics, for instance in chemistry and biology.


PhD students

Licentiate theses

Master theses


Research interests: a stringy web site. Check also links on the home page of the Mathematical Physics Group


Teaching: general public courses

Physics for poets


Teaching: undergraduate level


The 2010 MatFysA course at GU (Lp II)

Teaching: Master level (i.e. fourth year, see Master program for the whole program)

The 2011 Master course on String/M theory (Lp IV)

The 2010 Master course on String/M theory (Lp IV)

The 2009 Master course on String/M theory (Lp IV)

The NEW 2008 Master course on String/M theory and LHC physics (Lp IV)

The 2007 Master course on String/M theory (Lp IV)

The 2006 Master course on String/M theory (Lp IV)

The 2003 Master course on Gravitation and Cosmology (Lp II)

(NOTE: here you find the 2004 course given by Gabriele Ferretti (Lp II)

The 2004 Master course on Group theory and Lie algebra (Lp III)

The 2004 Master course on String/M theory (Lp IV)

The 2004 Master course in Astroparticle physics (Lp IV)

The 2005 Master course on Group theory and Lie algebra(Lp III)

The 2005 Master course on String/M theory (Lp IV)

The 2005 Master course in Astroparticle physics (Lp IV)

Are you interested in writing a Master thesis on strings, branes, M-theory, quantum gravity or perhaps (stringy) inflationary cosmology? Click here for possible topics!

Teaching: graduate level

The 2009/2010 PhD/MSc course on Group theory, Lie algebra and representations(Lp I-II)

Advanced String/M2 theory: Start January, 2008

Advanced String/M theory: Start September 5, 2007

Supersymmetry and pure spinors: 2006

Advanced String/M theory:1991-92

Supersymmetry and supergravity

Differential geometry and topology

Last modified May 11, 2006