Kinetic Factors in Affine Quantization and Their Role in Field Theory Monte Carlo

Abstract

Affine quantization, which is a parallel procedure with canonical quantization, needs to use its principal quantum operators, most simply $D=(PQ+QP)/2$ and $Q\ne 0$, to represent appropriate kinetic factors, normally $P^2$, which involve only one canonical quantum operator. The need for this requirement stems from the quantization of selected problems that require affine quantization to achieve valid Monte Carlo results. This task is resolved for introductory examples as well as examples that involve scalar quantum field theories.

arXiv comment13 pages, 1 table, 2 figures. arXiv admin note: text overlap with arXiv:2011.09862

References in corpus (4)

• Marginal triviality of the scaling limits of critical 4D Ising and ${\varphi }_4^4$ models
• Triviality of ${\phi }^4$ theory in a finite volume scheme adapted to the broken phase
• Low temperature acoustic polaron localization
• Monte Carlo evaluation of the continuum limit of the two-point function of the Euclidean free real scalar field subject to affine quantization

Cited by in corpus (5)

• Scaled Affine Quantization of Ultralocal ${\phi }_2^4$ a comparative Path Integral Monte Carlo study with Canonical Quantization
• Scaled Affine Quantization of ${\phi }_3^{12}$ is Nontrivial
• Thank The Quantum Realm For Nothing Ever Entering Into Black Holes
• Continuum limit of the Green function in scaled affine ${\phi }_4^4$ quantum Euclidean covariant relativistic field theory
• Scaled Affine Quantization of ${\phi }_4^4$ in the Low Temperature Limit