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
In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions...In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.展开更多
In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.
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.
文摘In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.
基金This work supported by the National Natural Science Foundation of China （Grand No. 10071003）
文摘In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.
