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FORM has been the essential tool to calculate the higher-order QCD beta function. The mathematical structure of multiple zeta values has been researched with dedicated FORM programs. [2] The software package FormCalc which is widely used in the physics community to calculate Feynman diagrams is built on top of FORM.
In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle of a manifold. In physics , it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagrangian mechanics and Hamiltonian mechanics (on the manifold Q {\displaystyle ...
The 1-form ω constructed in this way respects the transitions between overlapping sets, and therefore descends to give a globally defined 1-form on the principal bundle F G E. It can be shown that ω is a principal connection in the sense that it reproduces the generators of the right G action on F G E , and equivariantly intertwines the right ...
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
The full expanded form of the Standard Model Lagrangian. We can now give some more detail about the aforementioned free and interaction terms appearing in the Standard Model Lagrangian density. Any such term must be both gauge and reference-frame invariant, otherwise the laws of physics would depend on an arbitrary choice or the frame of an ...
[1] [2] [3] The fundamental understanding of structure functions in terms of QCD is one of the outstanding problems in hadron physics. Why do quarks form colourless hadrons with only two stable configurations, proton and neutron? One important step towards answering this question is to characterize the internal structure of the nucleon.
The theory of the strong interaction (i.e. quantum chromodynamics, QCD), to which many contributed, acquired its modern form in 1973–74 when asymptotic freedom was proposed [23] [24] (a development that made QCD the main focus of theoretical research) [25] and experiments confirmed that the hadrons were composed of fractionally charged quarks.
In elementary particle physics and mathematical physics, in particular in effective field theory, a form factor is a function that encapsulates the properties of a certain particle interaction without including all of the underlying physics, but instead, providing the momentum dependence of suitable matrix elements.