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This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
Mathematical consistency of the Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible [clarification needed] at energies above 1.4 TeV; [45] therefore, the LHC (designed to collide two 7 TeV proton beams) was built to answer the question of whether the Higgs boson actually exists ...
The book series was initiated in 1958 with the name New Mathematical Library by the Monograph Project of the School Mathematics Study Group (SMSG) with financing from the National Science Foundation. Anneli Cahn Lax was the editor-in-chief of the series, intended as mathematical expositions written by outstanding mathematicians for an audience ...
It was considered the most complete book written in quantum mechanics at the time of release. [2] [14] It was praised for its axiomatic approach. [2] A review by Jacob Tamarkin compared von Neumann's book to what the works on Niels Henrik Abel or Augustin-Louis Cauchy did for mathematical analysis in the 19th century, but for quantum mechanics ...
These spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics, machine learning, partial differential equations, and Fourier analysis. More generally, functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.
The first complete mathematical formulation of this approach, known as the Dirac–von Neumann axioms, is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces (which he called unitary spaces) in his 1927 classic paper and book.
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
Thus every object, from an elementary particle to atoms, molecules and on up to planets and beyond are subject to the uncertainty principle. The time-independent wave function of a single-moded plane wave of wavenumber k 0 or momentum p 0 is [ 11 ] ψ ( x ) ∝ e i k 0 x = e i p 0 x / ℏ . {\displaystyle \psi (x)\propto e^{ik_{0}x}=e^{ip_{0}x ...