Generalized Statistics in Quantum Field Theory.

Mitsuru Yamada

Andreas Wipf

Tian Yu Cao

Introduction: Conceptual issues in quantum field theory Part I. Philosophers' Interests in Quantum Field Theory: 1. Why are we philosophers interested in quantum field theory 2. Quantum field theory and the philosopher Part II. Three Approaches to the Foundations of Quantum Field Theory: 3. The usefulness of a general theory of quantized fields 4. Effective field theory in condensed matter physics 5. The triumph and limitations of quantum field theory 6. Comments Discussions Part III. Does Quantum Field Theory Need a Foundation: 7. Does quantum field theory need a foundation? Part IV. Mathematics, Statistical Mechanics and Quantum Field Theory: 8. Renormalization group theory: its basis and formulation in statistical physics 9. Where does quantum field theory fit into the big picture? 10. The unreasonable effectiveness of quantum field theory 11. Comment: the quantum field theory of physics and of mathematics Part V. Quantum Field Theory and Spacetime: Introduction 12. Quantum field theory and spacetime: formalism and reality 13. Quantum field theory of geometry 14. 'Localization' in quantum field theory: how much of QFT is compatible with what we know about spacetime 15. Comments VI. 16. What is quantum field theory and what did we think it was? 17. Comments Discussions Part VII.Renormalization Group: 18. What is fundamental physics? A renormalization group perspective 19. Renormalization group: an interesting yet puzzling idea Part VIII. Non-Abelian Gauge Theory: 20. Gauge fields, gravity and Bohm's theory 21. Is the Aharonov-Bohm effect local? Discussions Part IX. The Ontology of Particles or Fields: 22. The ineliminable classical face of quantum field theory 23. The logic of quanta 24. Do Feynman diagrams endorse a particle ontology? 25. On the ontology of QFT Part X. Panel Discussion.

Efim S. Fradkin, Igor Anatol'evich Batalin, G. A. Vilkovisky +1 more

Gianfausto Dell’Antonio, Oscar Wallace Greenberg, E. C. G. Sudarshan

ABS>Use of a quantum field theory obeying parastatistics to treat free particles is further examined. Relativistic quantum field theories independent of locality are noted to hold for paralocal fields, and the TCP theorem is generalized to paralocal fields. The following generalization of the connection of spin and statistics is demonstrated: given the choice between parabose and parafermi statistics, integral spin flelds must obey parabose, and odd halfintegral spin fields must obey parafermi statistics (D.C.W.)

Christian Brouder, Frédéric Patras

In quantum field theory (QFT), the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This simple property paves the way to the classical treatment of perturbative QFT. This is no longer the case in the presence of initial correlations, that is if the vacuum is replaced by a general state. As a consequence, the combinatorics of correlated systems such as the ones occurring in many-body physics is more complex than that of quantum field theory and the general theory has made very slow progress. Similar observations hold in statistical physics or quantum probability for the perturbation series arising from the study of non Gaussian measures. In this work, an analysis of the Hopf algebraic aspects of quantum field theory is used to derive the structure of Green functions in terms of connected and one-particle irreducible Greeen functions for perturbative QFT in the presence of initial correlations.