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In this chapter we introduce the problem of Triviality of the \(\varphi ^4\) Relativistic Euclidean Scalar Quantum Field Theory in four spacetime dimensions and how it can be overcome with Affine Quantization. How Affine Quantization offers the mathematical rigor necessary to prove the existence of Scalar Particles. The importance of infinities and of the number zero. The importance of the instrument of the Numerical Experiment which through the Monte Carlo method can solve exactly but numerically a Lattice Field Theory.

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Triviality of Four-Dimensional \(\varphi ^4\) Theory on the Lattice

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  • 发表日期：

    2025年

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  • Riccardo Fantoni

摘要

In this chapter we introduce the problem of Triviality of the \(\varphi ^4\) Relativistic Euclidean Scalar Quantum Field Theory in four spacetime dimensions and how it can be overcome with Affine Quantization. How Affine Quantization offers the mathematical rigor necessary to prove the existence of Scalar Particles. The importance of infinities and of the number zero. The importance of the instrument of the Numerical Experiment which through the Monte Carlo method can solve exactly but numerically a Lattice Field Theory.