(Supersymmetric) Kac-Moody Gauge Fields in 3+1 Dimensions

Lagrangians for gauge fields and matter fields can be constructed from the infinite dimensional Kac-Moody algebra and group. A continuum regularization is used to obtain such generic lagrangians, which contain new nonlinear and asymmetric interactions not present in gauge theories based on compact Lie groups. This technique is applied to deriving the Yang-Mills and Chern-Simons lagrangians for the Kac-Moody case. The extension of this method to D=4, N=(1/2,0) supersymmetric Kac-Moody gauge fields is also made.Comment: 21 pages, no figures, latex. Minor change

A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this `complex-action problem', which utilizes a factorization property of distribution functions. The basic idea is quite general, and it removes the so-called overlap problem completely. Here we apply the method to a nonperturbative study of superstring theory using its matrix formulation. In this particular example, the distribution function turns out to be positive definite, which allows us to reduce the problem even further. Our numerical results suggest an intuitive explanation for the dynamical generation of 4d space-time.Comment: 7 pages, 4 figures, PRD version somewhat extended from the original versio

Experimental Evidence for Quantum Structure in Cognition

We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.Comment: 12 pages, 3 figure

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl

Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory

Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a layer given form by an underlying classical deterministic process, incorporating essentially logical thought and its indeterministic version modeled by classical probability theory; (ii) a layer given form under influence of the totality of the surrounding conceptual landscape, where the different concepts figure as individual entities rather than (logical) combinations of others, with measurable quantities such as 'typicality', 'membership', 'representativeness', 'similarity', 'applicability', 'preference' or 'utility' carrying the influences. We call the process in this second layer 'quantum conceptual thought', which is indeterministic in essence, and contains holistic aspects, but is equally well, although very differently, organized than logical thought. A substantial part of the 'quantum conceptual thought process' can be modeled by quantum mechanical probabilistic and mathematical structures. We consider examples of three specific domains of research where the effects of the presence of quantum conceptual thought and its deviations from classical logical thought have been noticed and studied, i.e. economics, decision theory, and concept theories and which provide experimental evidence for our hypothesis.Comment: 14 page

Price of coupon bond options in a quantum field theory of forward interest rates

10.1016/j.physa.2006.04.021Physica A: Statistical Mechanics and its Applications370198-103PHYA

Interest rates in quantum finance: The Wilson expansion and Hamiltonian

10.1103/PhysRevE.80.046119Physical Review E - Statistical, Nonlinear, and Soft Matter Physics804-PLEE

Quantum field theory of treasury bonds

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics641 II016121/1-016121/16PLEE

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory

10.1103/PhysRevE.75.016703Physical Review E - Statistical, Nonlinear, and Soft Matter Physics751-PLEE

Kac-Moody gauge fields and matter fields in d dimensions

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics2713-4343-346PYLB