Petr Jizba

Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Faculty Member

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Papers by Petr Jizba

Observables in the Quantum Field Theory of neutrino mixing and oscillations

by Petr Jizba and Giuseppe Vitiello

We report about recent results on the Quantum Field Theory of neutrino mixing and oscillations. A... more

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Feynman checkerboard picture and neutrino oscillations

Journal of Physics: Conference Series, 2015

Option pricing and generalized statistics: density matrix approach

Recent Advances in Stochastic Modeling and Data Analysis, 2007

I present a path integral formulation of the density matrix for Rényi and Tsallis-Havrda-Charvát ... more I present a path integral formulation of the density matrix for Rényi and Tsallis-Havrda-Charvát statistics. As a practical application I derive the associated option pricing formula generalizing the Black-Scholes analysis for Gaussian stock fluctuations. Perturbation expansion around the Black-Scholes formula is performed and properties of the ensuing expansion are discussed.

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Observables in the Quantum Field Theory of neutrino mixing and oscillations

by Massimo Blasone and Petr Jizba

We report about recent results on the Quantum Field Theory of neutrino mixing and oscillations. A... more

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Towards information theory for q-nonextensive statistics without q-deformed distributions

Physica A: Statistical Mechanics and its Applications, 2006

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-... more In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for systems with embedded self-similarity and q-nonextensivity. We find that this entropy can be uniquely solved in terms of a one-parameter family of information measures. The corresponding entropy maximizer is expressible via a special function known under the name of the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and make some remarks on the possible applications.

Quantum fields with topological defects

by Massimo Blasone, Giuseppe Vitiello, and Petr Jizba

Construction of relativistic quantum fields in the framework of white noise analysis. Journal of ... more

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The emergence of Special and Doubly Special Relativity

In a previous paper [Phys.Rev.D82, 085016(2010)] we introduced a method for obtaining the exact F... more In a previous paper [Phys.Rev.D82, 085016(2010)] we introduced a method for obtaining the exact Feynman propagator of a relativistic particle (for both Klein-Gordon and Dirac case) from a superstatistical average over non-relativistic single-particle paths. We suggested that this method could offer new insights into the currently much debated issue of emergent relativity. In this paper we proceed further, showing that

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phenomenon?

by Petr Jizba and Fabio Scardigli

We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory ... more We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his pre-quantization scheme. We find that quantum mechanics might indeed have a fully deterministic underpinning by showing that Born's rule naturally emerges (i.e.,

Inflationary cosmology from quantum conformal gravity

by Petr Jizba and Fabio Scardigli

The European Physical Journal C, 2015

We analyze the functional integral for quantum Conformal Gravity and show that with the help of a... more We analyze the functional integral for quantum Conformal Gravity and show that with the help of a Hubbard-Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which in the weak-field sector of the broken phase induces a Starobinsky-type f (R)model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky's parameter and the cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with recent PLANCK and BICEP2 data.

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Superstatistics approach to path integral for a relativistic particle

Physical Review D, 2010

SMEARING DISTRIBUTIONS AND THEIR USE IN FINANCIAL MARKETS

Path Integrals — New Trends and Perspectives - Proceedings of the 9th International Conference, 2008

Quantum Field Theory of Topological Defects as Inhomogeneous Condensates

by Petr Jizba and Massimo Blasone

Basics and Highlights in Fundamental Physics - Proceedings of the International School of Subnuclear Physics, 2001

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Information Theory and Generalized Statistics

Lecture Notes in Physics, 2003

In this lecture we present a discussion of generalized statistics based on Rényi's, Fisher's and ... more In this lecture we present a discussion of generalized statistics based on Rényi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of generalized statistics to systems with (multi-)fractal structure are examined. 2 P. Jizba astronomy, geophysics, biology, medical diagnosis and economics. For the latest developments in classical MaxEnt the interested reader may consult ref.

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A framework for dynamical generation of flavor mixing

by Petr Jizba and Massimo Blasone

Journal of Physics: Conference Series, 2014

We present a dynamical mechanismà la Nambu-Jona-Lasinio [1] for the generation of masses and mixi... more We present a dynamical mechanismà la Nambu-Jona-Lasinio [1] for the generation of masses and mixing for two interacting fermion fields. The analysis is carried out in the framework introduced long ago by Umezawa et al. , in which mass generation is achieved via inequivalent representations, and that we generalize to the case of two generations. The method allows a clear identification of the vacuum structure for each physical phase, confirming previous results [3] about the distinct physical nature of the vacuum for fields with definite mass and fields with definite flavor. Implications for the leptonic sector of the Standard Model are briefly discussed.

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Dissipation, Emergent Quantization, and Quantum Fluctuations

by Giuseppe Vitiello, Massimo Blasone, and Petr Jizba

Lecture Notes in Physics, 2003

We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact... more We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The 't Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quantum features of the system, is analyzed and the quantum spectrum of the harmonic oscillator is shown to be originated from the dissipative character of the original classical deterministic system.

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Quantum Field Theory and Its Macroscopic Manifestations

by Giuseppe Vitiello, Massimo Blasone, and Petr Jizba

Physicists believe quantum fields to be the true protagonists of nature in the full variety of it... more Physicists believe quantum fields to be the true protagonists of nature in the full variety of its wonderful, manifold manifestations. Quantum field theory is the tool they created to fulfill their visionary dream of describing with a universal, unique language all of nature, be it single particles or condensed matter, fields or many-body objects. This is perhaps the first book on quantum field theory whose aim is to grasp and describe with rigor and completeness, but at the same time in a compelling, fascinating way, all the facets of the complex challenge it faces scientists with. It is a book that presents solutions but poses questions as well; hard, demanding yet fascinating; a book that can at the same time be used as a textbook and as a book of dreams that any scientist would like to make come true."

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Superpositions of probability distributions

Physical review. E, Statistical, nonlinear, and soft matter physics, 2008

Probability distributions which can be obtained from superpositions of Gaussian distributions of ... more Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v=sigma;{2} play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in v which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics.

Practical Approach to Construction of Internal Variables of Complex Self-organized Systems and Its Theoretical Foundation

Springer Proceedings in Complexity, 2013

Rényi transfer entropy and its application for intraday financial data

On the Role of Information Theoretic Uncertainty Relations in Quantum Theory

Uncertainty relations based on information theory for both discrete and continuous distribution f... more Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson-Schrödinger uncertainty relation and Kraus-Maassen Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson-Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.

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