Relationship between string theory and quantum field theory
Many first principles in quantum field theory are explained, or get further insight, in string theory: Note: formally, gauge symmetries in string theory are (at least in most cases) a result of the existence of a global symmetry together with the profound gauge symmetry of string theory, which is the symmetry of the worldsheet under a local change of coordinates and scales.
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
Interpretations of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real", and other matters. This question is of special interest to philosophers of physics, as physicists continue to show a strong interest in the subject. History of interpretations[edit] Main quantum mechanics interpreters An early interpretation has acquired the label Copenhagen interpretation, and is often used. Nature of interpretation[edit] An interpretation of quantum mechanics is a conceptual or argumentative way of relating between: Two qualities vary among interpretations: Concerns of Einstein[edit]
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. .
Schwinger–Dyson equation
The Schwinger–Dyson equations (SDEs), also known as the Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between Green functions in quantum field theories (QFTs). They are also referred to as the Euler–Lagrange equations of quantum field theories, since they are the equations of motion of the corresponding Green's function. They form a set of infinitely many functional differential equations, all coupled to each other, sometimes referred to as the infinite tower of SDEs. In his paper "The S-Matrix in Quantum electrodynamics",[1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach. Schwinger also derived an equation for the two-particle irreducible Green functions,[2] which is nowadays referred to as the inhomogeneous Bethe–Salpeter equation. Derivation[edit] , we have
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. 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. Quantities such as particle masses are stochastically calculated using techniques such as the Monte Carlo method. , where is the lattice action and . See also[edit]
EPR paradox
Albert Einstein The EPR paradox is an early and influential critique leveled against the Copenhagen interpretation of quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment which revealed that the accepted formulation of quantum mechanics had a consequence which had not previously been noticed, but which looked unreasonable at the time. According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually. The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. The EPR paper, written in 1935, was intended to illustrate that this explanation is inadequate. History of EPR developments[edit] Quantum mechanics and its interpretation[edit] Einstein's opposition[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. See also[edit] References and external links[edit]
