Extraordinary properties of functional integrals and groups of diffeomorphisms
- PDF / 640,294 Bytes
- 20 Pages / 612 x 792 pts (letter) Page_size
- 84 Downloads / 203 Views
traordinary Properties of Functional Integrals and Groups of Diffeomorphisms V. V. Belokurova, b, * and E. T. Shavgulidzea, ** a b
Moscow State University, Moscow, 119991 Russia
Institute for Nuclear Research, Russian Academy of Sciences, Moscow, 117312 Russia *e-mail: [email protected] **e-mail: [email protected]
Abstract―A review of the work of the authors is presented, in which corollaries of the quasi-invariance of functional integrals on the Wiener measure with respect to the action of a group of diffeomorphisms are studied, and the behavior of functional integrals with nonlinear nonlocal change of variables of integration is investigated as well. Using these substitutions, the functional integrals over discontinuous paths can be determined. The simplest models of the (Euclidean) quantum field theory are offered, in which the presence of hidden internal symmetries or the allowance for discontinuous paths in functional integrals leads to a number of paradoxical properties contradicting the conventional view. DOI: 10.1134/S1063779617020022
1. DEDICATION This work is dedicated to the blessed memory of the outstanding scholar and remarkable person, Vladimir Georgievich Kadyshevsky. The scope of his personality required setting of grand problems, and he accepted the challenge with his inherent courage and persistence. Still in his youth, V.G. Kadyshevsky began to deal with creation of a realistic model of the nonlocal quantum field theory, in which there is a fundamental dimensional parameter of the type of the elementary length or the curvature of momentum space. At the same time, he was brilliantly knowledgeable in the most diverse areas of contemporary theoretical highenergy physics and was always receptive to new ideas. With great respect, genuine interest, and caring attention, V.G. Kadyshevsky regarded the work of his colleges, both already famous and quite young scientists, offered very helpful advice, and, above all, inspiration. His memory and our deep gratitude will live forever in our hearts. 2. INTRODUCTION This work comprises a review of our works [1–7], in which corollaries of the infinite-dimensional symmetries for functional integrals of the quantum field theory are studied.
Section 3 is of a supplemental nature. Here, some data on the Wiener measure and groups of diffeomorphisms are given and the formulas are derived which define rules of transformation of the Wiener measure under the action of the group of diffeomorphisms. Section 4 shows that the quantum measures for a free massless particle and a free massive particle are equivalent within the accuracy of diffeomorphisms. Section 5 offers the generalization of the local quantum field theory taking into account the presence of hidden internal symmetries, namely, a model of quantum field theory is constructed on the space of loops, which in the local limit (when a loop is contracted to a point) is transformed to the local quantum field theory with converging Feynman diagrams. In Sections 6 and 7, general properties of nonlinear nonlocal cha
Data Loading...
