摘要:

AbstractTo explore in its full richness the topological possibilities of gauge fields one should allow for simultaneous presence of gravitational and Yang‐Mills ones. Thus if the integral topological indices of the Yang‐Mills field for a flat Euclidean base space is associated with the structure of the vacuum, one may ask among other questions of interest, how this spectrum might be modified when the base space itself has non trivial indices. Exact solutions ofSU(2) Yang‐Mills fields are presented for metrics corresponding to well‐known gravitational instantons. Such selfdual solutions, with vanishing energy monien‐tunl tensorTμvfor Euclidean signature of the base space, do not perturb the metric. Thus they provide solutions of the combined gravitational‐Y.M. system. New topological possibilities, such as finite actionSU(2) fields with fractional indices for many centre inetrics are displayed explicitly. As another type of possibility non selfdual, finite action solutions are constructed explicitly on Schwarzschild and de Sitter metrics, the solution being real in the first and complex in second case respectively. It is also shown how various meron type solutions in flat space can be derived systematically from a very simple static solution

ISSN:0015-8208    

DOI:10.1002/prop.2190350102

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

摘要:

AbstractMonopoles in the Bogomolny‐Prasad‐Sommerfield limit have been constructed, often using instanton like techniques, but separately starting all over again. It is possible to do better. The well known fact that (replacing the Higgs scalar Φ byAtof the Euclidean gauge potentials) such solutions can be considered as infinite action limits of selfdual Yang‐Mills field ones can be exploited more deeply and fruitfully. Instead of constructing one monopole (or one instanton) one can, in a single stroke construct an infinite sequence of instantons such that a monopole solution emerges practically trivially in a particularly simple scaling limit. Typically one constructs a single solution involving a parameter whose admissible values give the entire spectrum of indices for members of this sequence (chain). Then the rescaling is done through this parameter to obtain a finite energy but infinite action selfdual monopole. Thusin a comparable number of steps one obtains not only the monopoles but much more. The chains of instantons thus displayed have remarkable properties well worth studying even if one is not directly interesed in monopoles. I start by discussing examples of such fascinating special properties for the simplest sequence (or 1‐chain) leading in the limit to the PS monopole of unit charge. Then techniques are presented for building a hierarchy of such chains giving multicharged monopoles as limits. For the higher chains our constructions present remarkable fully explicit examples of instantons in the Atiyah‐Ward classes greater than one. The basic idea here is to use the de Sitter line element to construct “static” finiteaction solutions, which becomes possible due to a compactification of the

ISSN:0015-8208    

DOI:10.1002/prop.2190350103

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

摘要:

AbstractThe perturbative structure of a quantum field theory of the solid state, including allradiative corrections, is applied for the calculation of renormaiization factors and counterterms. After a general outline, approximation schemes for the explicit evaluation of renormalization parameters are developed.

ISSN:0015-8208    

DOI:10.1002/prop.2190350104

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

摘要:

AbstractThis work presents the results of a quantitative investigation of the “sum rule method” recently proposed by the author for calculating low‐lying energy levels. The system considered in detail is the circular Aharonov‐Bohm quantum billiard recently introduced by Berry and Robnik. Exact, expressions are derived for the spectral zeta function at positiveinteger values as a function of the magnetic flux. Using the zeta function for fixed angular momentum, we observe a very fast convergence to the exact ground state energy (“precocious conv

ISSN:0015-8208    

DOI:10.1002/prop.2190350105

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.2190350101

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY