Gamma matricesIn mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts.
Issues in anarchismAnarchism is generally defined as the political philosophy which holds the state to be undesirable, unnecessary and harmful as well as opposing authority and hierarchical organization in the conduct of human relations. Proponents of anarchism, known as anarchists, advocate stateless societies based on non-hierarchical voluntary associations. While anarchism holds the state to be undesirable, unnecessary and harmful, opposition to the state is not its central or sole definition.
Kähler manifoldIn mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil.
Pseudo-Riemannian manifoldIn differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike.
Social anarchismSocial anarchism, also known as left-wing anarchism or socialist anarchism, is the branch of anarchism that sees liberty and social equality as interrelated. It advocates for a social revolution to remove oppressive forms of hierarchy, such as capitalism and the state. In their place, social anarchists encourage social collaboration through mutual aid and envision non-hierarchical forms of social organization, such as voluntary associations.
Laissez-faireLaissez-faire (ˌlɛseɪˈfɛər ; from laissez faire lɛse fɛːʁ, let do) is a type of economic system in which transactions between private groups of people are free from any form of economic interventionism (such as subsidies or regulations). As a system of thought, laissez-faire rests on the following axioms: "the individual is the basic unit in society, i.e. the standard of measurement in social calculus; the individual has a natural right to freedom; and the physical order of nature is a harmonious and self-regulating system.
Stress–energy tensorThe stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.
Libertarianism in the United StatesIn the United States, libertarianism is a political philosophy promoting individual liberty. According to common meanings of conservatism and liberalism in the United States, libertarianism has been described as conservative on economic issues (economic liberalism) and liberal on personal freedom (civil libertarianism), often associated with a foreign policy of non-interventionism.
Complex manifoldIn differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
