An Etymological Dictionary of Astronomy and Astrophysics
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1) Excessive adherence to prescribed forms.
2) Math., Logic: → Formalized expression of a set of elements; the nature of such expression.
3) A philosophical view of mathematics in which mathematics, including the logic used in proofs, can be based on the formal manipulation of symbols irrespective of their meaning.

From → formal + → -ism.

A reformulation of classical mechanics that predicts the same outcomes as classical mechanics. → Hamiltonian dynamics.

→ Hamiltonian; → mechanics.

A reformulation of classical mechanics that describes the evolution of a physical system using → variational principle The formalism does not require the concept of force, which is replaced by the → Lagrangian function. The formalism makes the description of systems more simpler. Moreover, the passage from classical description to quantum description becomes natural. Same as → Lagrangian dynamics.

→ Lagrangian; → formalism.

An approximate version of → general relativity that applies when the → gravitational field is → weak, and the matter → velocity is → small. Post-Newtonian formalism successfully describes the gravitational field of the solar system. It can also be applied to situations involving compact bodies with strong internal gravity, provided that the mutual gravity between bodies is weak. It also provides a foundation to calculate the → gravitational waves emitted by → compact binary star systems, as well as their orbital evolution under radiative losses. The formalism proceeds from the Newtonian description and then, step by step, adds correction terms that take into account the effects of general relativity. The correction terms are ordered in a systematic way (from the largest effects to the smallest ones), and the progression of ever smaller corrections is called the → post-Newtonian expansion.

→ post-; → Newtonian; → formalism.

A mathematical analysis, based on → self-similarity, used to predict the → mass function of spherically collapsing → dark matter halos. The formalism assumes that the fraction of mass in halos more massive than M is related to the fraction of the volume in which the smoothed initial density field is above some threshold δ_cρ, where ρ is the average density of the Universe, with the volume encompassing a mass larger than M. A variety of smoothing → window functions and thresholds have been argued, but the most common is a top-hat window in real space and δ_c≅ 1.69. The Press-Schechter formalism provides a relatively good fit to the results of numerical simulations in cold dark matter theories.

First described by William H. Press and Paul Schechter's paper (1974, ApJ 187, 425); → formalism.