Invariant (physics)In theoretical physics, an invariant is an observable of a physical system which remains unchanged under some transformation. Invariance, as a broader term, also applies to the no change of form of physical laws under a transformation, and is closer in scope to the mathematical definition. Invariants of a system are deeply tied to the symmetries imposed by its environment. Invariance is an important concept in modern theoretical physics, and many theories are expressed in terms of their symmetries and invariants.
TheoryA theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
M-theoryM-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995 (M-Theory - Edward Witten (1995)). Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory.
Superstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories (Type I, Type IIA, Type IIB, HO and HE) are regarded as different limits of a single theory tentatively called M-theory.
Supersymmetric quantum mechanicsIn theoretical physics, supersymmetric quantum mechanics is an area of research where supersymmetry are applied to the simpler setting of plain quantum mechanics, rather than quantum field theory. Supersymmetric quantum mechanics has found applications outside of high-energy physics, such as providing new methods to solve quantum mechanical problems, providing useful extensions to the WKB approximation, and statistical mechanics.
String theoryIn physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string.
Lorentz groupIn physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry: The kinematical laws of special relativity Maxwell's field equations in the theory of electromagnetism The Dirac equation in the theory of the electron The Standard Model of particle physics The Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature.
GauginoIn supersymmetry theories of particle physics, a gaugino is the hypothetical fermionic supersymmetric field quantum (superpartner) of a gauge field, as predicted by gauge theory combined with supersymmetry. All gauginos have spin 1/2, except for gravitino (spin 3/2). In the minimal supersymmetric extension of the standard model the following gauginos exist: The gluino (symbol _gluino) is the superpartner of the gluon, and hence carries color charge. The gravitino (symbol _gravitino) is the supersymmetric partner of the graviton.
SfermionIn supersymmetric extension to the Standard Model (SM) of physics, a sfermion is a hypothetical spin-0 superpartner particle (sparticle) of its associated fermion. Each particle has a superpartner with spin that differs by 1/2. Fermions in the SM have spin-1/2 and, therefore, sfermions have spin 0. The name 'sfermion' was formed by the general rule of prefixing an 's' to the name of its superpartner, denoting that it is a scalar particle with spin 0. For instance, the electron's superpartner is the selectron and the top quark's superpartner is the stop squark.
Holonomic constraintsIn classical mechanics, holonomic constraints are relations between the position variables (and possibly time) that can be expressed in the following form: where are n generalized coordinates that describe the system (in unconstrained configuration space). For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic.
