A glass is disordered material like a viscous liquid and behaves mechanically like a solid. A glass is normally formed by supercooling the viscous liquid fast enough to avoid crystallization, and the liquid-glass transition occurs in diverse manners depending on the materials, their history, and the supercooling processes, among other factors. The glass transition in colloids, molecular systems, and polymers is studied worldwide. This book presents a unified theory of the liquid-glass transition on the basis of the two band model from statistical quantum field theory associated with the temperature Green’s function method. It is firmly original in its approach and will be of interest to researchers and students specializing in the glass transition across the physical sciences.

Key Features

  • Examines key theoretical problems of the liquid-glass transition and related phenomena
  • Clarifies the mechanism and the framework of the liquid-glass transition


Researchers, advanced students and professionals in physics, chemical engineering, mechanical engineering, materials science, and applied mathematics.

Table of Contents


Chapter 1. Introduction

1.1 The Structure of the Condensed States and the Quantum Regime

1.2 The Two Band Model for the Liquid-Glass Transition

1.3 Perspective of This Book


Chapter 2. Sound and Elastic Waves in the Classical Theory

2.1 Sound in the Classical Fluid Mechanics

2.2 Elastic Waves in the Classical Elastic Theory

2.3 Sound and Phonons in the Classical Microscopic Theory

2.4 The Kauzmann Entropy, the Vogel– Tamman– Fulcher Law and Specific Heat


Chapter 3. Fundamentals of Quantum Field Theory

3.1 The Number Representation and the Fock Space

3.2 An Example of Unitarily Inequivalent Representations; The Bogoliubov Transformation of Boson Operators

3.3 The Physical Particle Representation and the Dynamical Map

3.4 Free Physical Fields for Physical Particles

3.5 The Physical Particle Representation and Perturbation Theory

3.6 The Spectral Representations of Two-Particle Green’s Functions

3.7 Invariance, the Noether Current and the Ward-Takahashi Relations


Chapter 4. Temperature Green’s Functions

4.1 Definition of the Temperature Green’s Functions

4.2 Perturbation Theory and the Wick’s Theorem at Finite Temperature

4.3 Feynman Diagrams

4.4 Dyson’s Equation


Chapter 5. Real Time Green’s Functions and Temperature Green’s Functions

5.1 Various Kinds of Green’s Functions

5.2 Linear Response and Density Correlation Function

5.3 A Linear Response Theory at Finite Temperature


Chapter 6. The Structure of Glasses Associated with Phonons

6.1 The WT relations at finite temperature

6.2 The two band model and Green’s functions

6.3 The Nambu-Goldstone theorem and phonons


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About the author

Toyoyuki Kitamura

Affiliations and Expertise

Emeritus Professor, Nagasaki Institute of Applied Science, Nagasaki, Japan