Number theory and physics

examples

totally real field and CFT

• Huang, An, On Twisted Virasoro Operators and Number Theory 2009
  

• adele and idele

• ANALOGIES BETWEEN KNOTS AND PRIMES, 3-MANIFOLDS AND NUMBER RINGs
  
  • Masanori Morishita
• A general approach to quantum fields and strings on adeles
  
  • Bernard David Barkan Roth
• The Weil proof and the geometry of the adeles class space
  
  • Alain Connes (College de France), Caterina Consani (Johns Hopkins), Matilde Marcolli (MPI Bonn)
• Quantum field theory, Grassmannians, and algebraic curves
  
  • Edward Witten
• On p-adic and Adelic generalization of quantum field theory
  
  • Branko Dragovich

instanton numbers

• Stienstra, Jan. 2006. “Mahler Measure Variations, Eisenstein Series and Instanton Expansions.” In Mirror Symmetry. V, 38:139–150. AMS/IP Stud. Adv. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=2282958.

statistical mechanics

• From number theory to statistical mechanics: Bose-Einstein condensation in isolated traps
  
  • Authors: Siegfried Grossmann, Martin Holthaus
• Number theory, dynamical systems and statistical mechanics.
  
  • Andreas Knauf

 

related items

• Physics and algebras
• Modular invariance in math and physics
• Mock theta and physics
• Infinities in number theory and physics
• Representations of linear groups : an introduction based on examples from physics and number theory
• Physics of number fields
• Amplitudes and Periods conference
• Arithmetic Chern-Simons Theory

expositions

• Vergu, Polylogarithms and physical applications, 2013
• Vergu, Notes on Polylogarithms
• Cardy, John. 2010. “The Ubiquitous ‘C’: From the Stefan-Boltzmann Law to Quantum Information.” arXiv:1008.2331 (August 13). doi:10.1088/1742-5468/2010/10/P10004. http://arxiv.org/abs/1008.2331.
  • slides The ubiquitous c — from the Stefan-Boltzmann law to quantum information theory
• MATILDE MARCOLLI NUMBER THEORY IN PHYSICS
• http://physics.stackexchange.com/questions/414/number-theory-in-physics

articles

• Broadhurst, David, and Oliver Schnetz. “Algebraic Geometry Informs Perturbative Quantum Field Theory.” arXiv:1409.5570 [hep-Th], September 19, 2014. http://arxiv.org/abs/1409.5570.

web resources

• number theory and physics archive

conferences and workshops

• Number Theory and Physics at the Crossroads (11w5001)
• Polylogarithms as a Bridge between Number Theory and Particle Physics
• Low-dimensional Topology and Number Theory
  • http://www.birs.ca/birspages.php?task=displayevent&event_id=07w5052
  • http://www.birs.ca/workshops/2007/07w5052/report07w5052.pdf