When made explicit this is called the worldline formalism for computing the quantum field perturbation series. This is usually a sigma-model with parameter space the given graph and target space the spacetime on which the fields live for which the perturbation series computes the path integral. The amplitude assigned to a single graph with n n external edges is interpreted as the amplitude for n n “quanta” or “ particles” of the fields in question to interact in the way indicated by the graph.Ĭrucial for the motivation of the idea of string theory is the observation that this (renormalized) amplitude assigned to a graph is itself the correlator of a 1-dimensional quantum field theory on that graph: the “worldline quantum field theory” describing the (relativistic) quantum mechanics of these particles. The graphs are called Feynman diagrams, the numbers assigned to them are called ( renormalized) scattering amplitudes and the sum over graphs of (renormalized) amplitudes is the perturbation series or S-matrix. Recall that in quantum field theory one approach to make sense of the path integral is the perturbation series expansion, which interprets the path integral for the scattering amplitudes (the S-matrix) as a certain sum over graphs of certain numbers assigned to each graph. Perturbative string theory is something at least close to a categorification of the following description of perturbative quantum field theory in terms of sums over Feynman diagrams. Conceptually: From QFT worldline formalism Its interest for experimental high energy physics lies in the hypothesis that it provides a theory of everything in the sense of fundamental physics, but the jury on that is still out.īelow we indicate the basic idea and provide pointers to further details. Certainly it is, mathematically, a structure that contains in various limits a plethora of quantum field theories. String theory is a theory in fundamental physics. Fields medal (and other) work related to string theory.Elliptic genera, elliptic homology and tmf.String theory results applied elsewhere.Elliptic genera, elliptic cohomology and tmf tmf.Critical string theories and quantum anomalies.Conceptually: From QFT worldline formalism.Gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity super Poincaré Lie algebra, supergravity Lie 3-algebra, supergravity Lie 6-algebraĮinstein-Hilbert action, Einstein's equations, general relativityįirst-order formulation of gravity, D'Auria-Fre formulation of supergravity.string theory results applied elsewhere.Particle, relativistic particle, fundamental particle, spinning particle, superparticle Gauge group, gauge transformation, gauge fixing (2,1)-dimensional Euclidean field theory and elliptic cohomology (1,1)-dimensional Euclidean field theories and K-theory Perturbative quantum field theory, vacuum Mass, charge, momentum, angular momentum, moment of inertiaĬovariant phase space, Euler-Lagrange equationsĮxtended topological quantum field theory Physics, mathematical physics, philosophy of physics Surveys, textbooks and lecture notesĮxperiment, measurement, computable physics Twisted smooth cohomology in string theory Green-Schwarz mechanism, differential string structure,ĪdS/CFT correspondence, holographic principle gravity, supergravity, Yang-Mills theory, quantum gravity.
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