We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t...We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in the proof is the three-dimensional puzzle for an infinitely renormalizable quadratic polynomial.展开更多
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, hi...Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.展开更多
Viewing gravitational energy-momentum PG<sup style='margin-left:-7px;'>μ as equal by observation, but different in essence from inertial energy-momentum PI<sup style='margin-left:-7px;'>μ...Viewing gravitational energy-momentum PG<sup style='margin-left:-7px;'>μ as equal by observation, but different in essence from inertial energy-momentum PI<sup style='margin-left:-7px;'>μ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.展开更多
The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 5...The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 53</strong>, 5761 (1996)] cannot be employed for <em>all</em> Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S<span style="white-space:nowrap;"><sup><span style="white-space:normal;">′</span></sup><sub style="margin-left:-7px;">L</sub></span>. We lifted such limitation in [J. Phys. Comm. <strong>2</strong> 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT infinities. We provide here three examples of the application of our STDELI-extension to quantum field theory (A) the exact evaluation of an electron’s self energy to one loop, (B) the exact evaluation of QED’s vacuum polarization, and C) the <img src="Edit_a42ec50a-a738-42b3-beaa-ce9730d18cdb.png" alt="" />theory for six dimensions, that is non-renormalizable.展开更多
基金supported in part by grants from the National Natural Science Foundation of China and the NBRP of Chinasupported in part by grants from the National Natural Science Foundation of Chinathe PSC-CUNY and the Hundred Talents Program from the Chinese Academy of Sciences.
文摘We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in the proof is the three-dimensional puzzle for an infinitely renormalizable quadratic polynomial.
基金Supported by National Nature Science Foundation of China (10775059)
文摘Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.
文摘Viewing gravitational energy-momentum PG<sup style='margin-left:-7px;'>μ as equal by observation, but different in essence from inertial energy-momentum PI<sup style='margin-left:-7px;'>μ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.
文摘The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. <strong>B 40</strong>, 566 (1972);Il Nuovo Cim. <strong>B 12</strong>, 20 (1972);Phys. Rev. <strong>D 53</strong>, 5761 (1996)] cannot be employed for <em>all</em> Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S<span style="white-space:nowrap;"><sup><span style="white-space:normal;">′</span></sup><sub style="margin-left:-7px;">L</sub></span>. We lifted such limitation in [J. Phys. Comm. <strong>2</strong> 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT infinities. We provide here three examples of the application of our STDELI-extension to quantum field theory (A) the exact evaluation of an electron’s self energy to one loop, (B) the exact evaluation of QED’s vacuum polarization, and C) the <img src="Edit_a42ec50a-a738-42b3-beaa-ce9730d18cdb.png" alt="" />theory for six dimensions, that is non-renormalizable.
