9510140

Please download to get full document.

View again

of 160
9 views
PDF
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Document Description
5
Document Share
Documents Related
Document Tags
Document Transcript
    a  r   X   i  v  :   h  e  p  -   t   h   /   9   5   1   0   1   4   0  v   3   1   4   M  a  r   1   9   9   6 Ministry of Higher and Special Secondary Educationof the USSR Moscow State Lomonosov University Physics Faculty Division of Experimental and Theoretical Physics Manuscript 1 UDK 530.12:531.51 Ivan Grigoryevich AVRAMIDI Covariant Methods for the Calculation of the Effective Action in Quantum Field Theoryand Investigation of Higher–DerivativeQuantum Gravity (01.04.02 — Theoretical and Mathematical Physics)DISSERTATION for the Degree of Candidate of Sciencesin Physics and Mathematics Scientific Supervisor:Professor V. R. Khalilov Moscow – 1986 1 Translated by the author on October 1995. Some misprints in the srcinal text arecorrected. Available at @xxx.lanl.gov/hep-th/9510140  Contents Introduction21 Background field method in quantum field theory11 1.1 Generating functional, Green functions and the effective action111.2 Green functions of minimal differential operators. . . . . . . . 171.3 Divergences, regularization, renormalization and the renorma-lization group. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Technique for the calculation of De Witt coefficients and itsapplications25 2.1 Covariant expansions of field variables in curved space. . . . 252.2 Structure elements of covariant expansions. . . . . . . . . . . 322.3 Technique for the calculation of De Witt coefficients. . . . . . 402.4 De Witt coefficients a 3 and a 4 at coinciding points. . . . . . . 442.5 Effective action of massive scalar, spinor and vector fields inexternal gravitational field. . . . . . . . . . . . . . . . . . . . 53 3 Partial summation of the semiclassical Schwinger–De Wittexpansion58 3.1 Summation of asymptotic expansions. . . . . . . . . . . . . . 583.2 Covariant methods for the investigation of nonlocalities. . . . 613.3 Summation of the terms of first order in external fields. . . . 653.4 Summation of the terms of second order in external fields. . . 703.5 Summation of the terms without covariant derivatives of ex-ternal fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . 781  Contents 2 4 Higher–derivative quantum gravity88 4.1 Quantization of gauge field theories. Unique effective action. 884.2 One–loop divergences of higher–derivative quantum gravity. . 964.3 Off–shell one–loop divergences of the standard effective actionin arbitrary gauge and the divergences of the unique effectiveaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.4 Renormalization group equations and the ultraviolet asympto-tics of the coupling constants. . . . . . . . . . . . . . . . . . 1154.5 Effective potential of higher–derivative quantum gravity. . . . 123 5 Conclusion141Bibliography143  Introduction The classical theory of macroscopic gravitational phenomena, i.e., Einstein’sGeneral Relativity (GR) [1, 2], cannot be treated as a complete self–consistenttheory in view of a number of serious difficulties that were not overcome sincethe creation of GR [3].This concerns, first of all, the problem of space–time singularities, whichare unavoidable in the solutions of the Einstein equations [1–4]. Close to thesesingularities GR becomes incomplete as it cannot predict what is coming fromthe singularity. In other words, the causal structure of space–time breaksdown at the singularities [4].Another serious problem of GR is the problem of the energy of the grav-itational field [5], which was critically analyzed, in particular, in the papersof Logunov and collaborators [6–8]. In the papers [9, 10] a new relativistictheory of gravitation (RTG) was proposed. In RTG the gravitational fieldis described by a spin–2 tensor field on a basic Minkowski space–time. Suchan approach enables one to define in the usual way the energy–momentumtensor of the gravitational field and to obtain the usual conservation laws.The curved space–time in this approach is only an effective one that describesthe influence of the gravitational field on all the non–gravitational matter.Therein the “identity” (or geometrization) principle formulated in the papers[10, 11] is embodied.The difficulties of the classical theory have motivated the need to con-struct a quantum theory of gravitation. Also the recent progress towardsthe unification of all non–gravitational interactions [12] shows the need toinclude gravitation in a general scheme of an unified quantum field theory.The first problem in quantizing gravity is the construction of a covariantperturbation theory [13–21]. Einstein’s theory of gravitation is a typical non–Abelian gauge theory with the diffeomorphism group as a gauge group [14].3
Similar documents
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks