CONTENTS -- Preface -- Conference committees -- Group photo -- Part I History and Perspectives -- Remarks on the origin of path integration: Einstein and Feynman T. Sauer -- 1. Introduction -- 2. The Wheeler-Feynman Absorber Theory -- 3. Einstein and the Electromagnetic Arrow of Time -- 4. Path Integrals for Actions with No Hamiltonian -- 5. The Demise of the Early Context of Path Integration -- References -- Quo vadis, physica? M. Gutzwiller -- 1. Introduction -- 2. Some Input from Philosophy -- 3. The Short History of Physics -- 4. Quantum Physics, Relativity, and the Nucleus until 1957 -- 5. The Boom in Physics from 1957 to 2007 -- 6. Things to be Expected -- Round-table discussion: quo vadis, path integrals - new trends and perspectives? -- Part II Quantum Physics -- An appetizer: a sampler of main courses C. DeWitt-Morette -- 1. Introduction -- 2. When Symmetries Define a Path Integral -- A Basic Theorem on Spaces of Pointed Paths -- 3. Solutions of PDE Other Than Parabolic -- Spaces of Poisson Paths -- 4. A General Property of Volume Elements -- the Koszul Formula -- Acknowledgments -- References -- What does operator ordering have to do with the density of paths? L. S. Schulman -- 1. Introduction -- 2. The Quantum Hamilton-Jacobi Equation -- 3. The Equivalent c-Number Problem -- 4. Applications -- 4.1. The semiclassical propagator -- 4.2. The -function propagator -- 5. Discussion -- References -- Near action-degenerate periodic-orbit bunches: a skeleton of chaos A. Altland, P. Braun, F. Haake, S. Heusler, G. Knieper, and S. Mü ller -- 1. Introduction -- 2. Unstable Initial Value Problem vs Stable Boundary Value Problem -- 3. Self-Encounters -- 4. Orbit Bunches -- 5. Hierarchies of Bunches -- 6. Quantum Signatures of Bunches -- 7. Conclusion -- Acknowledgment -- References -- Path integration in the field of dispiration A. Inomata.

1. Introduction -- 2. Gauge Approach to the Dispiration -- 3. The Propagator -- 4. Energy Spectrum -- 5. Concluding Remarks -- References -- Real time path integrals in studies of quantum dots dynamics: non-monotonous decay rate and reappearance of Rabi rotations A. Vagov, M. D. Croitoru, V. M. Axt, T. Kuhn, and F. Peeters -- 1. Introduction -- 2. Model and Numerical Path-Integral Calculation -- 3. Results and Discussion -- 4. Conclusions -- Acknowledgments -- References -- Three useful bounds in quantum mechanics - easily obtained by Wiener integration H. Leschke and R. Ruder -- 1. Feynman-Kac Formula -- 2. Diamagnetic Inequality -- 3. Quasi-Classical Upper Bound on the Integrated Density of States in the Case of a Random Scalar Potential -- 4. A Simple Diamagnetic Monotonicity -- References -- Path-integral derivation of Lifshitz tails V. Sa-yakanit -- 1. Introduction -- 2. Model System -- 3. Density of States -- 4. Discussion -- References -- Feynman integrals as generalized functions on path space: things done and open problems L. Streit -- 1. Introduction: The Feynman "Integral" -- 2. How to Recognize a Generalized Function When You See One -- 3. Construction -- 4. Classes of Admissible Interactions -- 5. Boundary Value Problems -- 6. Beyond Perturbation Theory -- 7. A Glimpse at (E)QFT -- 8. Things to be Done -- References -- Accelerated path-integral calculations via e ective actions A. Balaˇz, I. Vidanović, A. Bogojević, and A. Belić -- 1. Introduction -- 2. Improved Discretized Effective Actions -- 3. Numerical Results -- 4. Conclusions -- Acknowledgments -- References -- Systematic speedup of energy spectra calculations for manybody systems I. Vidanović, A. Balaˇz, A. Bogojević, and A. Belić -- Acknowledgments -- References -- Geometric phase and chiral anomaly in path integral formulation K. Fujikawa -- 1. Second Quantization.

2. Hidden Local Gauge Symmetry -- 3. Non-Adiabatic Phase -- 3.1. Cyclic evolution -- 3.2. Non-cyclic evolution -- 4. Exactly Solvable Example -- 5. Chiral Anomaly -- References -- Phase space path integrals and their semiclassical approximations N. Kumano-go and D. Fujiwara -- 1. Introduction -- 2. Main Results -- References -- Gelfand-Yaglom type equation forWiener unconditional measure functional integral with x4 term in potential J. Boháˇcik and P. Preˇsnajder -- 1. Evaluation of x4 Wiener Functional Integral -- 1.1. One-dimensional integral -- 1.2. Gel'fand-Yaglom equation -- 2. Conclusions -- Acknowledgments -- References -- Coherent states for a quantum particle on a Mö bius strip D. J. Cirilo-Lombardo -- 1. Introduction -- 2. Abstract Coherent States -- 3. Physical Phase Space and Natural Quantization -- 4. Dynamics -- References -- Part III Quantum Field Theory -- Challenges to path-integral formulations of quantum theories R. Jackiw -- References -- Multivalued fields and third quantization H. Kleinert -- 1. Coordinate Transformations in Path Integrals -- 2. Multivalued Fields -- 3. Apparent First Order of Superconducting Transition -- 4. Second-Order Transition -- 5. Crystal Defects and the Melting Transition -- 6. Crystal Defects and Geometry -- References -- Gaussian equivalent representation of path integrals over a Gaussian measure G. V. Efimov -- 1. Introduction -- 2. Gaussian Equivalent Representation -- 3. Screening of the Coulomb Potential in Plasma -- References -- Path integral inspired gauge invariant infrared regularization A. A. Slavnov -- 1. Introduction -- 2. A Path-Integral Regularization -- 3. Canonical Quantization and Unitarity of Regularized Theory -- Acknowledgments -- References -- Causal signal transmission by interacting quantum fields L. I. Plimak, W. P. Schleich, and S. Stenholm.

1. Response of the Harmonic Oscillator -- 2. Response of Interacting Bosons -- References -- Rigorous functional integration with applications in QFT J. Lörinczi -- 1. Introduction -- 2. Functional Integration for Nelson's Model -- 3. Functional Integration for the Pauli-Fierz Model -- Acknowledgment -- References -- Stable extended string-vortex solitons I. L. Bogolubsky, A. A. Bogolubskaya, A. I. Bogolubsky, and S. L. Skorokhodov -- 1. Introduction -- 2. 2D Stable Solitons in the A3M Model -- Acknowledgments -- References -- Recent results for Yang-Mills theory restricted to the Gribov region J. A. Gracey -- 1. Introduction -- 2. Gribov-Zwanziger Lagrangian -- 3. Calculations -- 4. Discussion -- Acknowledgments -- References -- Mass spectra of the light and heavy mesons and the glueball G. Ganbold -- 1. Introduction -- 2. The Model -- 3. Meson Spectrum -- 4. Lowest Glueball State -- 5. Light Meson Decay Constants -- References -- Part IV Quantum Gravity -- Path integrals in quantum gravity: general concepts and recent developments C. Kiefer -- 1. Introduction -- 2. Euclidean versus Lorentzian Path Integrals -- 3. Perturbation Theory and Asymptotic Safety -- 4. Path Integrals and Canonical Quantum Gravity -- 5. Conclusion -- Acknowledgments -- References -- The emergence of (Euclidean) de Sitter space-time J. Ambjørn, A. Görlich, J. Jurkiewicz, and R. Loll -- 1. Introduction -- 2. The Macroscopic S4 Universe -- 3. Fluctuations Around the Four-Sphere -- 4. Discussion -- Acknowledgment -- References -- Functional integrals in a ne quantum gravity J. R. Klauder -- 1. Introduction -- 2. Affine Kinematical Variables -- 3. Affine Coherent States -- 4. Projection Operator Approach for Quantum Constraints -- 5. Continuous-Time Regularized Functional Integral Representation without/with Constraints -- 6. Hard-Core Picture of Nonrenormalizability.

References -- The role of Thomas-Fermi approach in neutron star matter R. Rufini -- 1. Introduction -- 2. Thomas-Fermi Model -- 3. White Dwarfs and Neutron Stars as Thomas-Fermi Systems -- 4. Relativistic Thomas-Fermi Equation -- 5. Essential Role of Non-Pointlike Nucleus -- 6. Nuclear Matter in Bulk: A ≈ 300 or A ≈ (mPlanck/mn)3 -- 7. Energetically Favorable Configurations -- 8. Conclusions -- Acknowledgments -- References -- A variational approach to the computation of the cosmological constant in a modified gravity theory R. Garattini -- 1. Introduction -- 2. One Loop Energy Regularization and Renormalization for a f (R) = R Theory -- 3. One Loop Energy Regularization and Renormalization for a Generic f (R) Theory in Hamiltonian Formulation -- References -- On nature of the cosmological constant L. V. Prokhorov -- References -- Dimensional reduction near the horizon Z. Haba -- 1. Introduction -- 2. Reflection Positivity and Euclidean Functional Integration -- 3. An Approximation at the Horizon -- 4. Green Functions Near the Horizon -- 5. Euclidean Free Fields Near the Horizon -- References -- Path integral for half-binding potentials as quantum mechanical analog for black hole partition functions D. Grumiller -- 1. Introduction and Statement of the Problem -- 2. Hamilton-Jacobi Counterterm for Half-Binding Potentials -- 3. Comparison with Black Hole Partition Functions -- Acknowledgments -- References -- Effective Lagrangians for noncommutative mechanics C. S. Acatrinei -- 1. Introduction -- 2. Path Integral -- 3. Discussion -- Acknowledgments -- References -- Part V Statistical Field Theory -- Functional integrals in physics: the main achievements J. Zinn-Justin -- 1. The Mystery of the Classical Variational Principle -- 1.1. Euler-Lagrange equations -- 1.2. The particle in a magnetic field -- 1.3. Electromagnetism and Maxwell's equations.

1.4. General relativity.