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Alkyl group. In organic chemistry, an alkyl group is an alkane missing one hydrogen. [1] The term alkyl is intentionally unspecific to include many possible substitutions. An acyclic alkyl has the general formula of −CnH2n+1. A cycloalkyl group is derived from a cycloalkane by removal of a hydrogen atom from a ring and has the general formula ...
Cycloalkyne. In organic chemistry, a cycloalkyne is the cyclic analog of an alkyne (−C≡C−). A cycloalkyne consists of a closed ring of carbon atoms containing one or more triple bonds. Cycloalkynes have a general formula CnH2n−4. Because of the linear nature of the C−C≡C−C alkyne unit, cycloalkynes can be highly strained and can ...
Cycloalkane. Ball-and-stick model of cyclobutane. In organic chemistry, the cycloalkanes (also called naphthenes, but distinct from naphthalene) are the monocyclic saturated hydrocarbons. [1] In other words, a cycloalkane consists only of hydrogen and carbon atoms arranged in a structure containing a single ring (possibly with side chains), and ...
Alkyl cycloalkane. Methylcyclopropane, the simplest alkyl cycloalkane. Alkyl cycloalkanes are chemical compounds with an alkyl group with a single ring of carbons to which hydrogens are attached according to the formula. C n H 2n. They are named analogously to their normal alkane counterpart of the same carbon count: methylcyclopropane ...
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 Standard Model is renormalizable and mathematically ...
The rigorous derivation of the Pauli equation follows from Dirac equation in an external field and performing a Foldy–Wouthuysen transformation [4] considering terms up to order (/). Similarly, higher order corrections to the Pauli equation can be determined giving rise to spin-orbit and Darwin interaction terms, when expanding up to order O ...
In particle physics, particle decay is the spontaneous process of one unstable subatomic particle transforming into multiple other particles. The particles created in this process (the final state) must each be less massive than the original, although the total mass of the system must be conserved.
A deeper understanding of the physical meaning and generalization of the renormalization process, which goes beyond the dilatation group of conventional renormalizable theories, came from condensed matter physics. Leo P. Kadanoff's paper in 1966 proposed the "block-spin" renormalization group. [3]