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M-theory. M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at the string theory conference at the University of Southern California in the summer of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Background[edit] Quantum gravity and strings[edit] One of the deepest problems in modern physics is the problem of quantum gravity. Number of dimensions[edit] In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time (later/earlier).

Despite the obvious relevance of four-dimensional spacetime for describing the physical world, there are several reasons why physicists often consider theories in other dimensions. Dualities[edit] Main articles: S-duality and T-duality A diagram of string theory dualities. And winding number in the dual description. . Superstring theory. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that incorporates fermions and supersymmetry. Since the second superstring revolution the five superstring theories are regarded as different limits of a single theory tentatively called M-theory, or simply string theory.

Background[edit] The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale. The development of a quantum field theory of a force invariably results in infinite (and therefore useless) probabilities. Evidence[edit] Superstring theory is based on supersymmetry. Extra dimensions[edit] See also: Why does consistency require 10 dimensions? Number of superstring theories[edit] The five superstring interactions. Grand Unified Theory. A Grand Unified Theory (GUT) is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant.

During the grand unification epoch, the gauge force separated from the gravitational force. Models that do not unify all interactions using one simple Lie group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well. Unifying gravity with the other three interactions would provide a theory of everything (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE. History[edit] Motivation[edit] Unification of matter particles[edit] Schematic representation of fermions and bosons in SU(5) GUT showing 5+10 split in the multiplets. SU(5)[edit] If. Supersymmetry. Gauge theory. Lattice gauge theory. Basics[edit] In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links.

In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links. That is, an element U of the compact Lie group G is assigned to each link. Hence to simulate QCD, with Lie group SU(3), there is a 3×3 special unitary matrix defined on each link. Yang–Mills action[edit] The Yang–Mills action is written on the lattice using Wilson loops (named after Kenneth G. There are many possible lattice Yang-Mills actions, depending on which Wilson loops are used in the action. . . , making computations more accurate. Measurements and calculations[edit] This result of a Lattice QCD computation shows a meson, composed out of a quark and an antiquark. . , where is the lattice action and . Other applications[edit] Lattice field theory. Just as in all lattice models, numerical simulation gives access to field configurations that are not accessible to perturbation theory, such as solitons.

Likewise, non-trivial vacuum states can be discovered and probed. The method is particularly appealing for the quantization of a gauge theory. Most quantization methods keep Poincaré invariance manifest but sacrifice manifest gauge symmetry by requiring gauge fixing. Only after renormalization can gauge invariance be recovered. See also[edit] References and external links[edit] Effective field theory. The renormalization group[edit] Presently, effective field theories are discussed in the context of the renormalization group (RG) where the process of integrating out short distance degrees of freedom is made systematic.

Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through a RG analysis. This method also lends credence to the main technique of constructing effective field theories, through the analysis of symmetries. If there is a single mass scale M in the microscopic theory, then the effective field theory can be seen as an expansion in 1/M. The construction of an effective field theory accurate to some power of 1/M requires a new set of free parameters at each order of the expansion in 1/M. This technique is useful for scattering or other processes where the maximum momentum scale k satisfies the condition k/M≪1.

Examples of effective field theories[edit] Electroweak interaction. In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 100 GeV, they would merge into a single electroweak force. Thus if the universe is hot enough (approximately 1015 K, a temperature exceeded until shortly after the Big Bang) then the electromagnetic force and weak force merge into a combined electroweak force. During the electroweak epoch, the electroweak force separated from the strong force. During the quark epoch, the electroweak force split into the electromagnetic and weak force. Formulation[edit] The pattern of weak isospin, T3, and weak hypercharge, YW, of the known elementary particles, showing electric charge, Q, along the weak mixing angle.

Lagrangian[edit] The where and. Quantum chromodynamics. In theoretical physics, quantum chromodynamics (QCD) is a theory of strong interactions, a fundamental force describing the interactions between quarks and gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A huge body of experimental evidence for QCD has been gathered over the years.

QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant. Terminology[edit] History[edit] Quantum field theory. Standard Model. The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world.[1] The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks.

Since then, discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2013), have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". Historical background[edit] The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. Overview[edit] Particle content[edit] Fermions[edit] Gauge bosons[edit] Higgs boson[edit] Main article: Higgs boson E.S.