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For example, asymptotic structure (cf. QCD jets) is a specific calculation in strong agreement with experiment, but nevertheless should fail by dint of Haag’s theorem. The general feeling is that this is not some calculation that was merely stumbled upon, but rather that it embodies a physical truth.
Manifest functions are the consequences that people see, observe or even expect. It is explicitly stated and understood by the participants in the relevant action. The manifest function of a rain dance, used as an example by Merton in his 1957 Social Theory and Social Structure, is to produce rain, and this outcome is intended and desired by people participating in the ritual.
In mathematics and theoretical physics, resummation is a procedure to obtain a finite result from a divergent sum (series) of functions.Resummation involves a definition of another (convergent) function in which the individual terms defining the original function are rescaled, and an integral transformation of this new function to obtain the original function.
In number theory, Tate's thesis is the 1950 PhD thesis of John Tate () completed under the supervision of Emil Artin at Princeton University.In it, Tate used a translation invariant integration on the locally compact group of ideles to lift the zeta function twisted by a Hecke character, i.e. a Hecke L-function, of a number field to a zeta integral and study its properties.
The function can be constructed from the partial computable function (,) described above and the s-m-n theorem: for each , () is the index of a program which computes the function (,). To complete the proof, let F {\displaystyle F} be any total computable function, and construct h {\displaystyle h} as above.
Quantum Field Theory A Modern Perspective. Springer. There are some review article about applications of the Schwinger–Dyson equations with applications to special field of physics. For applications to Quantum Chromodynamics there are R. Alkofer and L. v.Smekal (2001). "On the infrared behaviour of QCD Green's functions". Phys. Rep. 353 (5 ...
Risch developed a method that allows one to consider only a finite set of functions of Liouville's form. The intuition for the Risch algorithm comes from the behavior of the exponential and logarithm functions under differentiation. For the function f e g, where f and g are differentiable functions, we have
The moduli space of solutions to Hitchin's equations was constructed by Hitchin in the rank two case on a compact Riemann surface and was one of the first examples of a hyperkähler manifold constructed. The nonabelian Hodge correspondence shows it is isomorphic to the Higgs bundle moduli space, and to the moduli space of holomorphic connections.