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This led to the so-called 'tau–theta' problem: [13] what seemed to be the same particle (now called K +) decayed in two different modes, Theta to two pions (parity +1), Tau to three pions (parity −1). [12] The solution to this puzzle turned out to be that weak interactions do not conserve parity. [7]
where and are real numbers, is an integer, which is called the order of the integrator, and where = = = =.Note that each of the operators and provides a symplectic map, so their product appearing in the right-hand side of also constitutes a symplectic map.
Shortly after the Bevatron came into use, it was recognized that parity was not conserved in the weak interactions, which led to resolution of the tau-theta puzzle, the understanding of strangeness, and the establishment of CPT symmetry as a basic feature of relativistic quantum field theories.
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes.In 1947, when Kac and Feynman were both faculty members at Cornell University, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. [1]
Tau functions are an important ingredient in the modern mathematical theory of integrable systems, and have numerous applications in a variety of other domains. They were originally introduced by Ryogo Hirota [ 1 ] in his direct method approach to soliton equations, based on expressing them in an equivalent bilinear form.
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theta functions; the angle of a scattered photon during a Compton scattering interaction; the angular displacement of a particle rotating about an axis; the Watterson estimator in population genetics; ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents the first Chebyshev function in number theory; Theta role ...
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