Partition function (quantum field theory)In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams.
Quantum field theoryIn theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.
Feynman diagramIn theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula.
Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Scalar field theoryIn theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.
Perturbation theory (quantum mechanics)In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g.
Quantum gravityQuantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars as well as in the early stages of the universe moments after the Big Bang Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated.
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
Fock spaceThe Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H. It is named after V. A. Fock who first introduced it in his 1932 paper "Konfigurationsraum und zweite Quantelung" ("Configuration space and second quantization"). Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on.
Fock stateIn quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions.
Banach spaceIn mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
Fréchet spaceIn functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely differentiable functions are typical examples of Fréchet spaces, many of which are typically Banach spaces.
Wigner quasiprobability distributionThe Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics. The goal was to link the wavefunction that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions of a given quantum-mechanical wavefunction ψ(x).
Haplogroup R1aHaplogroup R1a, or haplogroup R-M420, is a human Y-chromosome DNA haplogroup which is distributed in a large region in Eurasia, extending from Scandinavia and Central Europe to Central Asia, southern Siberia and South Asia. While one genetic study indicates that R1a originated 25,000 years ago, its subclade M417 (R1a1a1) diversified c. 5,800 years ago. The place of origin of the subclade plays a role in the debate about the origins of Proto-Indo-Europeans.
Nintendo DSThe Nintendo DS is a handheld game console produced by Nintendo, released globally across 2004 and 2005. The DS, an initialism for "Developers' System" or "Dual Screen", introduced distinctive new features to handheld games: two LCD screens working in tandem (the bottom one being a touchscreen), a built-in microphone and support for wireless connectivity. Both screens are encompassed within a clamshell design similar to the Game Boy Advance SP.
Nintendo 3DSThe Nintendo 3DS is a handheld game console produced by Nintendo. The console was announced in March 2010 and unveiled at E3 2010 as the successor to the Nintendo DS. The system features backward compatibility with Nintendo DS video games. As an eighth-generation console, its primary competitor was Sony's PlayStation Vita.
RatRats are various medium-sized, long-tailed rodents. Species of rats are found throughout the order Rodentia, but stereotypical rats are found in the genus Rattus. Other rat genera include Neotoma (pack rats), Bandicota (bandicoot rats) and Dipodomys (kangaroo rats). Rats are typically distinguished from mice by their size. Usually the common name of a large muroid rodent will include the word "rat", while a smaller muroid's name will include "mouse". The common terms rat and mouse are not taxonomically specific.
Haplogroup R1bHaplogroup R1b (R-M343), previously known as Hg1 and Eu18, is a human Y-chromosome haplogroup. It is the most frequently occurring paternal lineage in Western Europe, as well as some parts of Russia (e.g. the Bashkirs) and across the Sahel in Central Africa, namely: Cameroon, Chad, Guinea Mauritania, Mali, Niger, Nigeria and Senegal (concentrated in parts of Chad with concentration in the Hausa Tribe and among the Chadic-speaking ethnic groups of Cameroon).
Brown ratThe brown rat (Rattus norvegicus), also known as the common rat, street rat, sewer rat, wharf rat, Hanover rat, Norway rat and Norwegian rat, is a widespread species of common rat. One of the largest muroids, it is a brown or grey rodent with a head and body length of up to long, and a tail slightly shorter than that. It weighs between . Thought to have originated in northern China and neighbouring areas, this rodent has now spread to all continents except Antarctica, and is the dominant rat in Europe and much of North America.
Outer spaceOuter space, commonly referred to simply as space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty; it is a near-perfect vacuum containing a low density of particles, predominantly a plasma of hydrogen and helium as well as electromagnetic radiation, magnetic fields, neutrinos, dust, and cosmic rays. The baseline temperature of outer space, as set by the background radiation from the Big Bang, is .
