Quantum field theory and its macroscopic manifestations Boson condensation, ordered patterns, and topological defects - Blasone, Massimo (Imperial College Press, 2011)
Includes bibliographical references and index
This book is a self-contained presentation of the quantum field theory of topological defects created during spontaneous symmetry breakdown phase transitions, with a particular emphasis on phenomenological issues of current interest
1. The structure of the space of the physical states. 1.1. Introduction. 1.2. The space of the states of physical particles. 1.3. The Weyl-Heisenberg algebra and the Fock space. 1.4. Irreducible representations of the canonical commutation relations. 1.5. Unitarily equivalent representations. 1.6. The Stone-von Neumann theorem. 1.7. Unitarily inequivalent representations. 1.8. The deformation of Weyl-Heisenberg algebra. 1.9. The physical particle energy and momentum operator. 1.10. The physical Fock space and the physical fields -- 2. Inequivalent representations of the canonical commutation relations. 2.1. Introduction. 2.2. Heisenberg fields, physical fields and the dynamical map. 2.3. Examples of inequivalent representations. 2.4. The Haag theorem and non-perturbative physics. 2.5. The momentum operator. 2.6. Time evolution and asymptotic limits. 2.7. Inequivalent representations in flavor mixing --
- 3. Spontaneous breakdown of symmetry and the Goldstone theorem. 3.1. Introduction. 3.2. Invariance and symmetry. 3.3. Irreducible representations of the symmetry group. 3.4. Symmetry and the vacuum manifold. 3.5. Boson transformation and inequivalent representations. 3.6. Spontaneous symmetry breaking and functional integrals. 3.7. The Goldstone theorem. 3.8. Spontaneous symmetry breaking in local gauge theories. 3.9. Finite volume effects. 3.10. Space-time dimensionality -- 4. Dynamical rearrangement of symmetry and macroscopic manifestations of QFT. 4.1. Introduction. 4.2. Dynamical rearrangement of symmetry. 4.3. The boson transformation theorem and the non-homogeneous boson condensation. 4.4. Group contraction and spontaneous symmetry breaking. 4.5. Quantum fluctuations and macroscopic stability --
- 5. Thermal field theory and trajectories in the space of the representations. 5.1. Introduction. 5.2. Doubling the degrees of freedom. 5.3. Thermo field dynamics : A brief introduction. 5.4. The q-deformed Hopf algebra and the doubling of the field degrees of freedom. 5.5. Free energy, entropy and the arrow of time. Intrinsic thermal nature of QFT. 5.6. Thermal field theory and the gauge field. 5.7. Boson condensation at finite temperature. 5.8. Trajectories in the space of representations