nLab
books and reviews in mathematical physics

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

The intention of this page is to list a wide choice of main books and comprehensive reviews in mathematical physics. The irrelevant repetitions and minor, too specialized and obsolete books in any major respect should be avoided. We avoid references for quantum groups as they are many and the main ones can be found at the quantum group entry; similarly we avoided the relevant books on Kac-Moody algebras and groups but included the books on related VOAs and the Pressley-Segal book.

Contents

Classical mathematical physics

Here PDEs, ODEs, and integral equation of mathematical physics, special functions, generalized functions, analytic functions, basic functional analysis, potential theory:

Classical mechanics

Mathematical introduction to quantum mechanics

On quantum mechanics:

Geometry and symmetries in classical and QM, quantization (but no QFT)

In addition to the geometrically written titles under classical mechanics above,

Lorentzian geometry and general relativity

Global aspects of the geometry of spacetimes:

After the introduction emphasis on asymptotics of spacetimes far from gravitation objects:

Despite its title the next monograph does not just present the Kerr spacetime, it illustrates many core features of GR with the Kerr spacetime as the prominent example:

Here is an introduction to spinors in GR:

while the classic reference for this is:

See also the above book by Ward and Wells; and mainstream theoretical physics gravity textbooks by Misner, Thorne and Wheeler; Schutz; Landau-Lifschitz vol. 2; Wald; Chandrasekhar etc. For the supergravity see the appropriate chapters in the above listed collection by Deligne et al. or the references listed at supergravity.

Integrable systems and solitons

On integrable systems and solitons:

Modern mathematical approaches to QFT and strings

On quantum field theory and string theory:

Branes (mathematical aspects)

Conformal field theory and vertex algebras

On conformal field theory and its chiral part (vertex operator algebras, chiral algebras):

The related subject of positive energy representations for loop groups is represented in unavoidable reference

Axiomatic quantum/statistical field theory and rigorous approaches to path integral

Other reference lists

category: reference