量子的な弦なので振幅は量子化され、1量子分のエネルギーを持った状態が第一励起状態となる。 In addition, this perspective led him to give a precise definition of entropy as the of the number of different states of the molecules also called microstates that give rise to the same macroscopic features. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. 1968年にヴェネツィアーノが発表したこの共鳴モデルは、レッジェ軌道を説明する公式を「散乱振幅」として表現した（ヴェネツィアーノ振幅）。 In the in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. In string theory, one must typically specify a fixed reference geometry for spacetime, and all other possible geometries are described as perturbations of this fixed one. Typically, such models are based on the idea of compactification. If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. Topological Field Theory, Primitive Forms and Related Topics. More precisely, Hawking's calculation seemed to conflict with one of the basic , which states that physical systems evolve in time according to the. 539—543• American Mathematical Society. Black holes are also important for theoretical reasons, as they present profound challenges for theorists attempting to understand the quantum aspects of gravity. It is a concrete realization of the , which has far-reaching implications for , and in physics, as well as the nature of the gravitational interaction. Second superstring revolution In 1995, at the annual conference of string theorists at the University of Southern California USC , gave a speech on string theory that in essence united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called. A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics. A classical result of states that there are exactly 27 straight lines that lie entirely on this surface. In the currently accepted models of stellar evolution, black holes are thought to arise when massive stars undergo , and many are thought to contain at their centers. ヴェネチアーノ散乱振幅はおよびによってすぐにN粒子の散乱振幅に一般化された。

もっと弦理論の衰退 [ ] しかし、ハドロンの弦理論は様々な欠陥を含んでいた。 In 1971, added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states. " Penrose also claims that the technical difficulty of modern physics forces young scientists to rely on the preferences of established researchers, rather than forging new paths of their own. In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate. The amplitude needed poles where the particles appear, on straight line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line—the — which was widely used in Regge theory. The same year, gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. One of the vibrational states of a string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. The Calabi—Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in , a branch of mathematics concerned with counting the numbers of solutions to geometric questions. This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family.。 弦理論 この節はなが全く示されていないか、不十分です。 太田信義『超弦理論・ブレイン・M理論』シュプリンガーフェアラーク東京〈シュプリンガー現代理論物理シリーズ〉、2002年。 。

もっと"Black hole entropy in M-theory". Subsequent work by Strominger, Vafa, and others refined the original calculations and gave the precise values of the "quantum corrections" needed to describe very small black holes. In most systems such as gases, the entropy scales with the volume. Smolin goes on to offer a number of prescriptions for how scientists might encourage a greater diversity of approaches to quantum gravity research. String theory has been used to construct a variety of models of particle physics going beyond the standard model. " Compatibility with dark energy No vacuum in the string theory landscape is known to support a metastable, positive , except possibly one unconfirmed model described by Kachru. The first person to add a to a theory of gravity was in 1914, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. 弦の場の理論はこのような状態の記述が出来ると期待され、実際に数値計算でならばポテンシャルが求められている。 On distance scales larger than the string scale, a string will look just like an ordinary particle, with its , , and other properties determined by the vibrational state of the string. また、上記のsチャンネルとtチャンネルは的に同一のものと見なす事ができる。 Main article: In mathematics, a is a rectangular array of numbers or other data. 一方、ジェフリー・チューのアプローチは分数チャージを導入せず、仮説上の点様の基本粒子ではなく実験的に計測可能なS-行列要素にのみ焦点を当ており、坂田模型やクォーク模型よりも主流とみなされていた。 The scattering of strings is most straightforwardly defined using the techniques of , but it is not known in general how to define string theory. Speaking at a string theory conference in 1995, Edward Witten made the surprising suggestion that all five superstring theories were in fact just different limiting cases of a single theory in eleven spacetime dimensions. 189• Although this function appears in a branch of mathematics which seems very different from the theory of finite groups, the two subjects turn out to be intimately related. 13—14• However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition. して記事の信頼性向上にご協力ください。

もっとThe Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. Physicists often study analogous to the electromagnetic field which live on the worldvolume of a brane. Randall, Lisa; Sundrum, Raman 1999. Unlike in quantum field theory, string theory does not have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach. This is a theoretical result which relates string theory to other physical theories which are better understood theoretically. T双対性との兼ね合いから、全く自由に見える開弦も、全空間を満たすD25ブレーンに繋がる事を要請される。 そして、それらはすべてではないことが明らかになった。 Witten's announcement drew together all of the previous results on S- and T-duality and the appearance of higher dimensional branes in string theory. The theory has also received striking support from observations of the cosmic microwave background, the radiation that has filled the sky since around 380,000 years after the Big Bang. In 1975, Stephen Hawking published a calculation which suggested that black holes are not completely black but emit a dim radiation due to quantum effects near the. The flurry of activity that began at this time is sometimes called the. These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure. and Vipul Periwal discovered that string perturbation theory was divergent. For example, the type I theory includes both open strings which are segments with endpoints and closed strings which form closed loops , while types IIA, IIB and heterotic include only closed strings. Partly because of theoretical and mathematical difficulties and partly because of the extremely high energies needed to test these theories experimentally, there is so far no experimental evidence that would unambiguously point to any of these models being a correct fundamental description of nature. Speculative scientific ideas fail not just when they make incorrect predictions, but also when they turn out to be vacuous and incapable of predicting anything. There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. Each of these different shapes corresponds to a different possible universe, or "vacuum state", with a different collection of particles and forces. In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. Ooguri, Hirosi; Strominger, Andrew; Vafa, Cumrun 2004. Working with experimental data, R. Weinberg suggested that there might be a huge number of possible consistent universes, each with a different value of the cosmological constant, and observations indicate a small value of the cosmological constant only because humans happen to live in a universe that has allowed intelligent life, and hence observers, to exist. By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. One property of this boundary is that, within a small region on the surface around any given point, it looks just like , the model of spacetime used in nongravitational physics. ただし、弦が内部構造を持たない実体であるという制限から、状態の数は減る。 Bekenstein—Hawking formula In the branch of physics called , is a measure of the randomness or disorder of a physical system. "Viscosity in strongly interacting quantum field theories from black hole physics". Connections to mathematics In addition to influencing research in , string theory has stimulated a number of major developments in. Despite much work on these problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of its details. In a viable model of particle physics, the compact extra dimensions must be shaped like a. 彼らは弦の長さを10 -35mオーダーの微小なものとし、弦の運動する時空を10次元とした。 The was started by in the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. Unification of superstring theories A schematic illustration of the relationship between , the five , and eleven-dimensional. These issues have led some in the community to criticize these approaches to physics, and to question the value of continued research on string theory unification. While these approaches might eventually find support in observational data such as measurements of the cosmic microwave background, the application of string theory to cosmology is still in its early stages. The result was widely advertised by , leading to construct a that had the property of Dolen—Horn—Schmid duality, later renamed world-sheet duality. The first is 's , a theory that explains the force of and the structure of at the macro-level. In the 20th century, two theoretical frameworks emerged for formulating the laws of physics. ハドロンの弦理論 [ ] レッジェ理論 1950年代から1960年代に渡って、強い相互作用をするかつてなく高いの粒子が多く発見された。 One of the major achievements of contemporary group theory is the , a mathematical theorem which provides a list of all possible finite simple groups. In the 1960s, and discovered that the make families called with masses related to spins in a way that was later understood by , and to be the relationship expected from rotating strings. from the original on 15 November 2020. The exhibits finite simple groups as the building blocks for all finite groups. The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings. In his book , physicist of the claims that this is the principal weakness of string theory as a theory of quantum gravity, saying that string theory has failed to incorporate this important insight from general relativity. しかしこれら空間のコンパクト化やブレーンの配位などを用いて、一つの理論に対して無数ともいえる「真空状態」が導かれ、弦はそれぞれの真空で異なった振る舞いをする。

もっと184• However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. The resulting looks like a solid. 彼らは、を表現したオイラー形式のモデルを振動する一次元の弦とする物理的解釈を提示した。

もっと"Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL 2, Z invariance in string theory". During the transition, the atoms behave in an unusual way. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes. "Hidden conformal symmetry of the Kerr black hole". 崩壊後の状態は、Dブレーンがないため開弦が存在できず、もはや弦での記述が不可能となる。 "Vacuum configurations for superstrings". Einstein introduced a , while much later Brans and Dicke added a scalar component to gravity. It is generally believed that finite groups are too diverse to admit a useful classification. Interaction in the quantum world: of point-like or a swept up by closed in string theory. In 1926, the Swedish physicist gave of the unobservable extra dimension—it is wrapped into a small circle. It is also not clear whether there is any principle by which string theory selects its , the physical state that determines the properties of our universe. These particles obey the usual rules of quantum mechanics and in particular evolve in a unitary fashion, so the black hole must also evolve in a unitary fashion, respecting the principles of quantum mechanics. Indeed, in 1998, Strominger argued that the original result could be generalized to an arbitrary consistent theory of quantum gravity without relying on strings or supersymmetry. 2-形式ゲージ粒子は、粒子が持つ電荷と結合するゲージ粒子の拡張で、弦が持つストリングチャージと結合する。 そのプログラムはと呼ばれ、を根本的に考えなおすものであった。 The exact properties of this particle are not fixed by the theory but should ultimately be derived from a more fundamental theory such as string theory. Thus string theory is a theory of quantum gravity. One important example of a matrix model is the BFSS matrix model proposed by , , , and in 1997. ハイゼンベルクは強い相互作用をする粒子は事実上広がりを持つであると提唱し、広がりのある相対論的粒子については物理法則の適用に困難があるため、彼は点の観念はスケールでは成立しないとすることを提案した。 Weinberg, Steven 1987. String theory as it is currently understood has an enormous number of vacuum states, typically estimated to be around 10 500, and these might be sufficiently diverse to accommodate almost any phenomenon that might be observed at low energies. In the s-channel, the two particles annihilate to make temporary intermediate states that fall apart into the final state particles. Connes, Alain; Douglas, Michael; Schwarz, Albert 1998. Despite its remarkable success in explaining a wide range of physical phenomena, the standard model cannot be a complete description of reality. It later developed into , which posits a connection called between bosons and the class of particles called. String theorist Leonard Susskind has argued that string theory provides a natural anthropic explanation of the small value of the cosmological constant. In the late 1970s, mathematicians and noticed that certain numbers arising in the analysis of the monster group namely, the dimensions of its are related to numbers that appear in a formula for the j-function namely, the coefficients of its. それら粒子のは のを持つ点様粒子のものとは大きく異なっていて、この違いは小さなが原因と考えるには大きすぎた。 ユニタリティは散乱を決定するのに高エネルギーの振る舞いに関する余分な仮定を必要としたため、この提案はあまり注目されなかった。 In collaboration with several other authors in 2010, he showed that some results on black hole entropy could be extended to non-extremal astrophysical black holes. " In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that the M should stand for "magic", "mystery", or "membrane" according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known. Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten was skeptical of the role of membranes in the theory. Nekrasov, Nikita; Schwarz, Albert 1998. This idea plays an important role in attempts to develop models of real world physics based on string theory, and it provides a natural explanation for the weakness of gravity compared to the other fundamental forces. Originally, these results of Candelas were justified on physical grounds. Regardless of whether Calabi—Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences. While there has been progress toward these goals, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of details. The physics of the quark—gluon plasma is governed by a theory called , but this theory is mathematically intractable in problems involving the quark—gluon plasma. ハイゼンベルクは、この問題に対する解決策は実験によって計測される観測可能な量に焦点を当てることであると考えた。

もっとis the branch of theoretical physics in which physicists construct realistic models of nature from more abstract theoretical ideas. and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Joseph Polchinski 2005. Witten noted that the effective description of the physics of D-branes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and had earlier discovered in terms of the location of the branes. 14—15• Bekenstein, Jacob 1973. どのような理論が得られるか、特に我々の4次元時空に相当するものが得られるのか、については、弦理論の主要な関心事である。 ; Duncan, John; Harvey, Jeffrey 2014. Lian, Bong; Liu, Kefeng; Yau, Shing-Tung 1999b. 296• "Strong-weak coupling duality in four-dimensional string theory". これに加え、重力子の見かけ上の運動方程式はほぼになり、が与える重力場の解が弦理論の古典解となる。 物理学者たちはこの弦理論の発展の余地を過小評価していたため、シュワルツおよびScherkは弦理論は流行するのに失敗したと議論していた。 Despite its success in explaining many observed features of the universe including galactic , the relative abundance of light elements such as and , and the existence of a , there are several questions that remain unanswered. , and further developed the covariant quantization of the superstring using conformal field theory techniques. In a review of Smolin's book, string theorist Joseph Polchinski writes [Smolin] is mistaking an aspect of the mathematical language being used for one of the physics being described. "Instantons on noncommutative R 4 and 2,0 superconformal six dimensional theory". Main article: In addition to being an idea of considerable theoretical interest, string theory provides a framework for constructing models of real world physics that combine general relativity and particle physics. For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In particular, they used mirror symmetry to show that a six-dimensional Calabi—Yau manifold can contain exactly 317,206,375 curves of degree three. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices. 一般相対論とは独立に、弦理論からT双対性を用いて、通常の空間方向を体積0の空間と対応させる事によって得られるは、ブラックブレーンの弦理論による説明であるとされる。 場の量子論では場というもので作用を書き下し、それを摂動展開する事によってファインマンルールを得るが、弦理論でのこれに相当する定式化、はと吉川圭二による提唱以来、様々な研究が重ねられてきたが、未完成である。 1974年、およびJoel Scherk 、そして独立には、弦振動のの様な振る舞いを研究し、それらの性質が厳密に（仮説上の重力の"メッセンジャー"粒子である）の性質と合致することを発見した。

もっと