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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.
The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general renormalizable Lagrangian from its particle (field) content that observes these symmetries.
In fluids, the phonon is longitudinal and it is the Goldstone boson of the spontaneously broken Galilean symmetry.In solids, the situation is more complicated; the Goldstone bosons are the longitudinal and transverse phonons and they happen to be the Goldstone bosons of spontaneously broken Galilean, translational, and rotational symmetry with no simple one-to-one correspondence between the ...
Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. [1] They are the fundamental objects of quantum field theory. Many families and sub-families of elementary particles exist. Elementary particles are classified according to their spin.
However, in Higgs' view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work, [68]: 6 while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose mathematical rigour is absent from the other two papers, and a massive particle may exist ...
For a non-relativistic system consisting of a finite number of distinguishable particles, the component systems are the individual particles. In the presence of quantum entanglement , the quantum state of the composite system cannot be factored as a tensor product of states of its local constituents; Instead, it is expressed as a sum, or ...
The term "particle" in this context refers to gaseous particles only (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium. [1] The energies of such particles follow what is known as Maxwell–Boltzmann statistics , and the statistical distribution of speeds is derived by equating particle ...
In particular, this means that a system of N interacting particles in 3 dimensions is described by one vector whose components in a basis where all the X are diagonal is a mathematical function of 3N-dimensional space describing all their possible positions, effectively a much bigger collection of values than the mere collection of N three ...