Exotic smoothness and particle physics

Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.Comment: 8 pages, pure LaTeX, Lecture given at the conference Particle Physics and Astrophysics in the Standard Model and Beyond, Bystra (Poland), September 199

Exotic Smoothness and Astrophysics

The problem of possible astrophysical consequences of the existence of exotic differential structures on manifolds is discussed. It is argued that corrections to the curvature of the form of a source like terms should be expected in the Einstein equations if they are written in the "wrong" differential structure. Examples of topologically trivial spaces on which exotic differential structures act as a source of gravitational force even in the absence of matter are given. Propagation of light in the presence of such phenomena is also discussed. A brief review of exotic smoothness is added for completeness.Comment: Talk given at XXXIII International Conference of Theoretical Physics: "Matter to the Deepest: Recent Developments in Physics of Fundamental Interactions

Particle physics from the noncommutative geometry point of view

Recent development in noncommutative geometry generalization of gauge theory is reviewed. The mathematical apparatus is reduced to minimum in order to allow the non-mathematically oriented physicists to follow the development in the interesting field of research. (Lectures presented at the Silesian School of Theoretical Physics: Standard Model and Beyond'93, Szczyrk (Poland), September 1993.)Comment: 16 pages, LaTeX file, BI-TP 93/6

Giffen paradoxes in quantum market games

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes in this new formalism is discussed.

Quantum Games and Programmable Quantum Systems

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.

Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle

We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot of common with quantum description of the harmonic oscillator. The approach has roots in the recently developed quantum game theory and quantum computing. A quantum anthropic principle is formulated. (final version published in Acta Phys.Pol.B,32(2001)3873-3879)

Quantum diffusion of prices and profits

We discuss the time evolution of quotation of stocks and commodities and show that quantum-like correction to the orthodox Bachelier model may be important. Our analysis shows that traders act as a sort of (quantum) tomograph and their strategies can be reproduced from the corresponding Wigner functions. The proposed interpretation of the chaotic movement of market prices imply that Orstein-Uhlenbeck corrections to the Bachelier model should qualitatively matter for large $\gamma$ scales. We also propose a solution to the currency preference paradox.