Principles of phase structures in particle physics / Hildegard Meyer-Ortmanns, Thomas Reisz.

Includes bibliographical references and index.

Print version record.

Preface -- 1. Introduction -- 2. General background from statistical physics. 2.1. Generalities. 2.2. Generating functional, n-point correlations and effective potentials. 2.3. The molecular-mean field approximation. 2.4. Renormalization group. 2.5. Finite-size scaling analysis for second-order phase transitions. 2.6. Finite-size scaling analysis for first-order phase transitions -- 3. Field theoretical framework for models in particle physics. 3.1. The standard model in limiting cases I: spin models as a guideline for the phase structure of QCD. 3.2. The standard model in limiting cases II: phase transitions in the electroweak part of the standard model. 3.3. A primer to lattice gauge theory -- 4. Analytic methods on the lattice and in the continuum. 4.1. Convergent versus asymptotic expansions. 4.2. Linked cluster expansions in more detail. 4.3. Renormalization, perturbation theory and universality at zero temperature -- the continuum limit. 4.4. Weak coupling expansion at finite temperature. 4.5. Constraint effective potential and gap equations. 4.6. Dimensional reduction at high temperature. 4.7. Flow equations of Polchinski -- 5. Numerical methods in lattice field theories. 5.1. Algorithms for numerical simulations in lattice field theories. 5.2. Pitfalls on the lattice. 5.3. Pure gauge theory: the order of the SU(3)-deconfinement transition. 5.4. Including dynamical fermions. 5.5. Thermodynamics on the lattice. 5.6. Interface tensions. 5.7. Other lattice actions for QCD and further reading -- 6. Effective actions in the continuum. 6.1. Postulating effective actions for QCD. 6.2. QCD and dysprosium. 6.3. The chiral transition in chiral perturbation theory. 6.4. Mass sensitivity of the chiral transition. 6.5. A network of gluonic strings. 6.6. Further reading -- 7. Phenomenological applications to relativistic heavy-ion collisions. 7.1. The QCD transition in the lab. 7.2. Signatures sensitive to the nature of the phase transition.

The phase structure of particle physics shows up in matter at extremely high densities and/or temperatures as they were reached in the early universe, shortly after the big bang, or in heavy-ion collisions, as they are performed nowadays in laboratory experiments. In contrast to phase transitions of condensed matter physics, the underlying fundamental theories are better known than their macroscopic manifestations in phase transitions. These theories are quantum chromodynamics for the strong interaction part and the electroweak part of the Standard Model for the electroweak interaction. It is their non-Abelian gauge structure that makes it a big challenge to predict the type of phase conversion between phases of different symmetries and different particle contents. The book is about a variety of analytical and numerical tools that are needed to study the phase structure of particle physics. To these belong convergent and asymptotic expansions in strong and weak couplings, dimensional reduction, renormalization group studies, gap equations, Monte Carlo simulations with and without fermions, finite-size and finite-mass scaling analyses, and the approach of effective actions as supplement to first-principle calculations.

English.

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