Quantum Field Theory A Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields
Résumé
A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator , no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian exists and that the corresponding *algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the quantum field theory model is Lorentz covariant. CONTENT CHAPTER I. § 1. INTRODUCTION. § 2. NON CONSERVATIVE EXTENSION OF THE MODEL THEORETICAL NONSTANDARD ANALYSIS. § 2.1. External Non-Archimedean Field ℝ # * by using Cauchy Completion of the Internal Non-Archimedean Field ℝ. * § 2.2. Hyper Infinite Sequences and Series of ℝ * #-Valued Functions. § 2.3. The #-Derivatives and Riemann #-Integral of ℝ * #-Valued Functions : → ℝ * #. § 2.4. The ℝ * #-Valued #-Exponential Function an ℝ * #-Valued Trigonometric Functions- ! ,-"#. § 2.5. ℝ * " #-Valued Schwartz Distributions. § 3. A NON-ARCHIMEDEAN METRIC SPACES ENDOWED WITH ℝ * " #-VALUED METRIC. § 4. LEBESGUE #-INTEGRATION OF ℝ * " #-VALUED FUNCTIONS. § 5. A NON-ARCHIMEDEAN BANACH SPACES ENDOWED WITH ℝ * " #-VALUED NORM. § 5.1. Semigroups on Non-Archimedean Banach Spaces and Their Generators. § 5.2. Hypercontractive semigroups. § 5.3. Strong #-convergence in the generalized sense.
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