From stochastic differential equations to quantum field theory
نویسنده
چکیده
Covariant stochastic partial (pseudo)-differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field theory is constructed by solving the analysed equations. The associated random cosurface models are discussed and some elementary properties of them are outlined.
منابع مشابه
Non–commutative (quantum) Probability, Master Fields and Stochastic Bosonization
In this report we discuss some results of non–commutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and physics including: q–deformed and free central limit theorems; the description of the master (i.e. central limit) field in matrix models along the recent Singer su...
متن کاملQuantum-theoretical treatments of three-photon processes
We perform and compare different analyses of triply degenerate four-wave mixing in the regime where three fields of the same frequency interact via a nonlinear medium with a field at three times the frequency. As the generalized Fokker-Planck equation ~GFPE! for the positive-P function of this system contains third-order derivatives, there is no mapping onto genuine stochastic differential equa...
متن کاملContinuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of ...
متن کاملStochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are assumed to have linear growth. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differentia...
متن کاملStochastic Schrodinger equations
A derivation of stochastic Schrödinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system’s quantum state given the observations made. This estimate satisfies a stoch...
متن کامل