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
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.
