出版時(shí)間:2008-8 出版社:科學(xué) 作者:布拉欽 頁(yè)數(shù):513
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前言
對(duì)于國(guó)內(nèi)的物理學(xué)工作者和青年學(xué)生來(lái)講,研讀國(guó)外優(yōu)秀的物理學(xué)著作是系統(tǒng)掌握物理學(xué)知識(shí)的一個(gè)重要手段。但是,在國(guó)內(nèi)并不能及時(shí)、方便地買到國(guó)外的圖書(shū),且國(guó)外圖書(shū)不菲的價(jià)格往往令國(guó)內(nèi)的讀者卻步,因此,把國(guó)外的優(yōu)秀物理原著引進(jìn)到國(guó)內(nèi),讓國(guó)內(nèi)的讀者能夠方便地以較低的價(jià)格購(gòu)買是一項(xiàng)意義深遠(yuǎn)的工作,將有助于國(guó)內(nèi)物理學(xué)工作者和青年學(xué)生掌握國(guó)際物理學(xué)的前沿知識(shí),進(jìn)而推動(dòng)我國(guó)物理學(xué)科研和教學(xué)的發(fā)展。 為了滿足國(guó)內(nèi)讀者對(duì)國(guó)外優(yōu)秀物理學(xué)著作的需求,科學(xué)出版社啟動(dòng)了引進(jìn)國(guó)外優(yōu)秀著作的工作,出版社的這一舉措得到了國(guó)內(nèi)物理學(xué)界的積極響應(yīng)和支持,很快成立了專家委員會(huì),開(kāi)展了選題的推薦和篩選工作,在出版社初選的書(shū)單基礎(chǔ)上確定了第一批引進(jìn)的項(xiàng)目,這些圖書(shū)幾乎涉及了近代物理學(xué)的所有領(lǐng)域,既有闡述學(xué)科基本理論的經(jīng)典名著,也有反映某一學(xué)科專題前沿的專著。在選擇圖書(shū)時(shí),專家委員會(huì)遵循了以下原則:基礎(chǔ)理論方面的圖書(shū)強(qiáng)調(diào)“經(jīng)典”,選擇了那些經(jīng)得起時(shí)間檢驗(yàn)、對(duì)物理學(xué)的發(fā)展產(chǎn)生重要影響、現(xiàn)在還不“過(guò)時(shí)”的著作(如:狄拉克的《量子力學(xué)原理》)。反映物理學(xué)某一領(lǐng)域進(jìn)展的著作強(qiáng)調(diào)“前沿”和“熱點(diǎn)”,根據(jù)國(guó)內(nèi)物理學(xué)研究發(fā)展的實(shí)際情況,選擇了能夠體現(xiàn)相關(guān)學(xué)科最新進(jìn)展,對(duì)有關(guān)方向的科研人員和研究生有重要參考價(jià)值的圖書(shū)。這些圖書(shū)都是最新版的,多數(shù)圖書(shū)都是2000年以后出版的,還有相當(dāng)一部分是2006年出版的新書(shū)。因此,這套叢書(shū)具有權(quán)威性、前瞻性和應(yīng)用性強(qiáng)的特點(diǎn)。由于國(guó)外出版社的要求,科學(xué)出版社對(duì)部分圖書(shū)進(jìn)行了少量的翻譯和注釋(主要是目錄標(biāo)題和練習(xí)題),但這并不會(huì)影響圖書(shū)“原汁原味”的感覺(jué),可能還會(huì)方便國(guó)內(nèi)讀者的閱讀和理解?! 八街?,可以攻玉”,希望這套叢書(shū)的出版能夠?yàn)閲?guó)內(nèi)物理學(xué)工作者和青年學(xué)生的工作和學(xué)習(xí)提供參考,也希望國(guó)內(nèi)更多專家參與到這一工作中來(lái),推薦更多的好書(shū)。
內(nèi)容概要
Dyson和Wigner最先成功地將隨機(jī)矩陣應(yīng)用到物理學(xué)中,經(jīng)過(guò)六七十年的發(fā)展,現(xiàn)在它在物理學(xué)中的應(yīng)用越來(lái)越廣泛,并且已經(jīng)滲透到了現(xiàn)代數(shù)學(xué)、物理學(xué)的很多新興領(lǐng)域,是理論物理學(xué)家的重要數(shù)學(xué)工具。隨機(jī)矩陣?yán)碚撓嚓P(guān)的數(shù)學(xué)方法能夠解決更多的問(wèn)題,而且方式更加靈活,在物理學(xué)中的應(yīng)用也更加深入,可以用來(lái)計(jì)算介觀系統(tǒng)的通用關(guān)系。它在無(wú)序系統(tǒng)和量子混沌領(lǐng)域也有一些新的應(yīng)用,并且通過(guò)建立新的矩陣模型,在二維引力和弦以及非阿貝爾規(guī)范理論方面取得了重要進(jìn)展。 本書(shū)由本領(lǐng)域的杰出學(xué)者撰寫(xiě),系統(tǒng)闡述了相關(guān)的理論知識(shí)。適合對(duì)隨機(jī)矩陣處理物理問(wèn)題感興趣的研究生和科研人員參考。
書(shū)籍目錄
PrefaceRandom Matrices and Number TheoryJ.P. Keating 1 Introduction 2 ζ(1/2+it)and logζ(1/2+it) 3 Characteristic polynomials of random unitary matrices 4 Other compact groups 5 Families of L-functions and symmetry 6 Asymptotic expansionsReferences2D Quantum Gravity, Matrix Models and Graph CombinatoricsP. Di Francesco 1 Introduction 2 Matrix models for 2D quantum gravity 3 The one-matrix model I: large N limit and the enumeration of planar graphs 4 The trees behind the graphs 5 The one-matrix model II:topological expansions and quantum gravity 58 6 The combinatorics beyond matrix models: geodesic distance in planar graphs 7 Planar graphs as spatial branching processes 8 ConclusionReferencesEigenvalue Dynamics, Follytons and Large N Limits of MatricesJoakim Arnlind, Jens HoppeReferencesRandom Matrices and Supersymmetry in Disordered SystemsK.B. Efetov 1 Supersymmetry method 2 Wave functions fluctuations in a finite volume. Multifractality 3 Recent and possible future developments 4 SummaryAcknowledgementsReferencesHydrodynamics of Correlated SystemsAlexander G.Abanoy 1 Introduction 2 Instanton or rare fluctuation method 3 Hydrodynam ic approach 4 Linearized hydrodynamics or bosoflization 5 EFP through an asymptotics of the solution 6 Free fermions 7 Calogero-Sutherland model 8 Free fermions on the lattice 9 ConclusionAcknowledgementsAppendix:Hydrodynamic approach to non-Galilean invariant systemsAppendix:Exact results for EFP in some integrable modelsReferencesQCD,Chiral Random Matrix Theory and IntegrabilityJ.JM.Verbaarschot 1 Summarv 2 IntrodUCtion 3 OCD 4 The Dirac spectrum in QCD 5 Low eflergy limit of QCD 6 Chiral RMT and the QCD Dirac spectrum 7 Integrability and the QCD partition function 8 QCD at fin ite baryon density 9 Full QCD at nonzero chemical potential 10 ConclusionsAcknowledgementsReferencesEUClidean Random Matrices:SOlved and Open ProblemsGiorgio Parisi 1 Introduction 2 Basic definitions 3 Physical motivations 4 Field theory 5 The simplest case 6 PhononsReferencesMatrix Models and Growth Processes3A.Zabrodin 1 Introduction 2 Some ensembles of random matrices with cornplex eigenvalues 3 Exact results at finite N 4 Large N limit 5 The matrix model as a growth problemReferencesMatrix Models and Topological StringsMarcos Marino 1 Introduction 2 Matrix models 3 Type B topological strings and matrix models 4 Type A topological strings, Chern-Simons theory and matrix models 366ReferencesMatrix Models of Moduli SpaceSunil Mukhi 1 Introduction 2 Moduli space of Riemann surfaces and its topology 3 Quadratic differentials and fatgraphs 4 The Penner model 5 Penner model and matrix gamma function 6 The Kontsevich Model 7 Applications to string theory 8 ConclusionsReferencesMatrix Models and 2D String TheoryEmil J. Martinec 1 Introduction 2 An overview of string theory 3 Strings in D-dimensional spacetime 4 Discretized surfaces and 2D string theory 5 An overview of observables 6 Sample calculation: the disk one-point function 7 Worldsheet description of matrix eigenvalues 8 Further results 9 Open problemsReferencesMatrix Models as Conformal Field TheoriesIvan K. Kostov 1 Introduction and historical notes 2 Hermitian matrix integral: saddle points and hyperelliptic curves 3 The hermitian matrix model as a chiral CFT 4 Quasiclassical expansion: CFT on a hyperelliptic Riemann surface 5 Generalization to chains of random matricesReferencesLarge N Asymptotics of Orthogonal Polynomials from Integrability to Algebraic GeometryB. Eynard 1 Introduction 2 Definitions 3 Orthogonal polynomials 4 Differential equations and integrability 5 Riemann-Hilbert problems and isomonodromies 6 WKB-like asymptotics and spectral curve 7 Orthogonal polynomials as matrix integrals 8 Computation of derivatives of F(0) 9 Saddle point method 10 Solution of the saddlepoint equation 11 Asymptotics of orthogonal polynomials 12 ConclusionReferences
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