This monograph provides an introduction to deformations of Poincaré symmetries focusing on models with a Lie group momentum space and associated non-commutative space-times. The emphasis is put on the emergence of such structures from quantum gravity, their mathematical features described in terms of Hopf algebras and applications to particle kinematics and field theory. Part I of this work focuses on the link between gravity and deformed symmetries in the case of 2+1 and 3+1 space-time dimensions. Part II is devoted to the description of classical particles with group valued momenta, their phase spaces and kinematics. The last part of these notes provides an introduction to the basic features of classical and quantum field theory on κ-Minkowski space-time, the prototypical example of non-commutative space-time exhibiting deformed Poincaré symmetry. The text, being the first providing a detailed overview of these topics, is primarily intended for researchers and graduate students interested in non-commutative field theories and quantum gravity phenomenology.

This volume provides a detailed discussion of the mathematical aspects and physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.

Since 1984, a series of regional conferences on mathematical physics has been organized by physicists from Iran, Pakistan and Turkey to promote the research in mathematical and theoretical physics in the region. This volume, which derives from the XI Regional Conference on Mathematical Physics, comprises 8 review and 44 research articles on the most significant topics in mathematical and theoretical physics such as astrophysics and cosmology, conformal field theory, high energy physics, general relativity and plasma physics. The review articles are comprehensive and self-contained and report on the most important developments in the corresponding subjects. Each review article provides a complete list of references, which is especially useful for graduate students who are just starting their research activities; even ambitious undergraduates in physics can use these review papers as useful background material to go further into the subject and explore the research literature. They are contributed by prominent senior scientists: M Moniez (Laboratoire de l'Accelerateur Lineare, France) and V Sahni (Inter-University Centre for Astronomy and Astrophysics (IUCAA), India) in Astrophysics and Cosmology, W Nahm (Dublin Institute for Advanced Studies (DIAS), Ireland) in Conformal Field Theory, J Lukierski (University of Wroclaw, Poland) in Mathematical Physics, Riazuddin and Fayyazuddin (Quaid-i-Azam University, Pakistan) in High Energy Physics, N Dadhich (Inter-University Centre for Astronomy and Astrophysics (IUCAA), India) and A Qadir (National University of Science and Technology, Pakistan) in General Relativity, and N Tsintsadze (Tbilisi State University, Georgia) in Plasma Physics. Contents:Astrophysics and Cosmology:Does Transparent Hidden Matter Generate Optical Scintillation? (M Moniez)Galactic MACHO Budget: Problems and Possible Solution with the Abundant Brown Dwarfs (S Rahvar)The Mysterious Nature of Dark Energy (V Sahni)Condensed Matter and Statistical Physics:Two-Band Ginzburg-Landau Theory and Its Application to Recently Discovered Superconductors (I N Askerzade)Charge and Magnetization Plateaux in Strongly Correlated Systems (A Langari)Exactly Solvable Problems for Two-Dimensional Excitons (D G W Parfitt & M E Portnoi)High Energy Physics — Phenomenology:SUL(4) x U(1) Model for Electroweak Unification (Fayyazuddin)Some Remarks on Neutrino Mass Matrix (Riazuddin)General Relativity and Quantum Gravity:Probing Universality of Gravity (N Dadhich)Observing Black Holes (P De Paolis et al.)Constraint Algebra in Causal Loop Quantum Gravity (F Shojai & A Shojai)Mathematical Physics:Quantum Deformations of Relativistic Symmetries: Some Recent Developments (J Lukierski)Thermodynamics Bethe Ansatz (TBA) (W Nahm)Hidden Property of Extended Jordanian Twists for Lie Superalgebras (V N Tolstoy)Noncommutative Field Theory and String Theory:Exact Wilsonian Effective Superpotential for Noncommutative N = 1 Supersymmetric U(1) (F Ardalan & N Sadooghi)Aspects of Noncommutative Gauge Theories and Their Commutative Equivalents (R Banerjee)Plasma Physics:Relativistic Thermodynamics of the Strong Magnetized Dense Electron Plasma (N L Tsintsadze)and other papers Readership: Researchers in mathematical physics, theoretical physics, high energy physics, astrophysics, astronomy, cosmology and condensed matter physics. Keywords:Mathematical Physics;String Theory;Plasma Physics;CosmologyKey Features:Includes eight high quality review articles on various subjects in physics, such as astrophysics and cosmology, conformal field theory, mathematical physics, high energy physics, general relativity and plasma physics, contributed by prominent physicistsUseful for advanced graduate students and active researchers in physics

Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries. The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus. The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory and Brownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity.

The Max Born Symposia started in 1991 and have been held once or twice a year in different places in Lower Silesia. The scientific topics of the Symposia are closely related with front-line research subjects in theoretical physics. This volume deals with new concepts of symmetries in the theory of fundamental intersections as well as integrable dynamical systems.

The Max Born Symposia started in 1991 and have been held once or twice a year in different places in Lower Silesia. The scientific topics of the Symposia are closely related with front-line research subjects in theoretical physics. This volume deals with new concepts of symmetries in the theory of fundamental intersections as well as integrable dynamical systems. Contents:Noncommutative Geometry and Quantum GroupsParticles, Strings, Superbranes and Their SUSY ExtensionsIntegrable Models and Related Topics Readership: Theoretical, high-energy and mathematical physicists. Keywords:Symmetries;Fundamental Intersections;Integrable Dynamical Systems;Theoretical Physics;High Energy Physics;Mathematical Physics

In recent years nonlinear and irreversible quantum mechanics is becoming increasingly important because of the availability of precision experiments. There are new and successful attempts to understand quantum irreversibility. The development of generalized symmetries has to led to new families of evolution equations for pure and mixed states. On the one hand, this timely symposium covers nonlinear and irreversible quantum mechanics, the theory of quantization methods, causality and various problems important in this context. On the other hand, it reports the development of quantum group symmetries, and of methods to construct deformed quantum mechanical evolution equations like the q-deformed Schrödinger equations.