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Geometrical Methods in Mathematical Physics Bernard F. Schutz
Publisher: Cambridge University Press

I am looking to learn/study up on differential geometry (including n-forms, tensors, etc) and perhaps group theory so as to better understand the mathematics behind some of the physics that I'm interested in (General Relativity, and the foundations of Quantum Mechanics with extensions perhaps into QFT). Geometrical methods of mathematical physics (Bernard F. Differential Geometrical Methods in Mathematical Physics : PDF eBook Download. While Brouwer's and other preintuitionists' reasons for intuitionistic mathematics were philosophical in nature, there is today a vibrant community of mathematicians, logicians, computer scientists, and even the odd physicist, who work with intuitionistic mathematics . It's the mathematics of infinitesimal calculus, brought forward to the 20th century by Anders Kock and Bill Lawvere under the name Synthetic Differential Geometry (SDG), or Smooth Infinitesimal Analysis. All attempts for nearly three decades, firmly establishes many theorems that had assumed it and paves the way for progress in understanding underlying mathematical structures and possible connections to physics," according to an article published in the Institute for Advanced Study's summer 2010 newsletter. I'm looking for 2 books maybe that could serve . Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics. But for QCD Path integrals have rightfully become the dominant way to describe physics of quantum fields and their strength turned out to be even more obvious in theories with non-Abelian gauge symmetries (Yang-Mills symmetries much like conformal symmetries on the worldsheet etc. Most of our reasons for believing the standard model are based on perturbative quantization of gauge fields, and for this it's true that geometrical methods are not strictly necessary. The ICM cited Ngô "for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods. March 11th, 2013 reviewer Leave a comment Go to comments.