Self-energyIn quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy , and represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and its environment. In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero.
Supersymmetric gauge theoryIn theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion. A gauge theory is a field theory with gauge symmetry. Roughly, there are two types of symmetries, global and local. A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent.
Realcompact spaceIn mathematics, in the field of topology, a topological space is said to be realcompact if it is completely regular Hausdorff and it contains every point of its Stone–Čech compactification which is real (meaning that the quotient field at that point of the ring of real functions is the reals). Realcompact spaces have also been called Q-spaces, saturated spaces, functionally complete spaces, real-complete spaces, replete spaces and Hewitt–Nachbin spaces (named after Edwin Hewitt and Leopoldo Nachbin).
Compactification (physics)In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic. Compactification plays an important part in thermal field theory where one compactifies time, in string theory where one compactifies the extra dimensions of the theory, and in two- or one-dimensional solid state physics, where one considers a system which is limited in one of the three usual spatial dimensions.
String field theoryString field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes. In most string field theories, this expansion is encoded by a classical action found by second-quantizing the free string and adding interaction terms.
Swampland (physics)In physics, the term swampland refers to effective low-energy physical theories which are not compatible with quantum gravity. This is in contrast with the so-called "string theory landscape" that are known to be compatible with string theory, which is believed to be a consistent quantum theory of gravity. In other words, the Swampland is the set of consistent-looking theories with no consistent ultraviolet completion with the addition of gravity.
Ultraviolet divergenceIn physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at infinitesimal distances. Since an infinite result is unphysical, ultraviolet divergences often require special treatment to remove unphysical effects inherent in the perturbative formalisms. In particular, UV divergences can often be removed by regularization and renormalization.
Particle physics and representation theoryThere is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe.
Dimensional reductionDimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in D spacetime dimensions can be redefined in a lower number of dimensions d, by taking all the fields to be independent of the location in the extra D − d dimensions. For example, consider a periodic compact dimension with period L. Let x be the coordinate along this dimension. Any field can be described as a sum of the following terms: with An a constant.
Pseudocompact spaceIn mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded. Many authors include the requirement that the space be completely regular in the definition of pseudocompactness. Pseudocompact spaces were defined by Edwin Hewitt in 1948. For a Tychonoff space X to be pseudocompact requires that every locally finite collection of non-empty open sets of X be finite.
