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New observables in topological instantonic field theories
ITEP, Moscow.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2011 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, Vol. 61, no 10, 1868-1880 p.Article in journal (Refereed) Published
Abstract [en]

Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type for the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on the linking of points.

The new "arbitrary jump" observables may be used to construct correlation functions computing, e.g., the linking numbers of cycles, as we illustrate on Hopf fibration.

We expect that such observables could be generalized in an interesting way to instantonic topological theories in all dimensions.

Place, publisher, year, edition, pages
2011. Vol. 61, no 10, 1868-1880 p.
Keyword [en]
Topological quantum mechanics, Geometric field theory, Topological field theory, Equivariant cohomologies, Integrated observables
National Category
Physical Sciences
Research subject
Physics with specialization in Elementary Particle Physics
URN: urn:nbn:se:uu:diva-123191DOI: 10.1016/j.geomphys.2011.04.020ISI: 000294314300008OAI: oai:DiVA.org:uu-123191DiVA: diva2:312945
Available from: 2010-04-26 Created: 2010-04-26 Last updated: 2011-09-22Bibliographically approved
In thesis
1. Yang-Mills Theory in Gauge-Invariant Variables and Geometric Formulation of Quantum Field Theories
Open this publication in new window or tab >>Yang-Mills Theory in Gauge-Invariant Variables and Geometric Formulation of Quantum Field Theories
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In Part I we are dealing with effective description of Yang-Mills theories based on gauge-invarint variables. For pure Yang-Mills we study the spin-charge separation varibles. The dynamics in these variables resembles the Skyrme-Faddeev model. Thus the spin-charge separation is an important intermediate step between the fundamental Yang-Mills theory and the low-energy effective models, used to model the low-energy dynamics of gluons. Similar methods may be useful for describing the Electroweak sector of the Standard Model in terms of gauge-invariant field variables called supercurrents.

We study the geometric structure of spin-charge separation in 4D Euclidean space (paper III) and elaborate onconnection with gravity toy model. Such reinterpretation gives a way to see how effective flat background metric is created in toy gravity model by studying the appearance of dimension-2 condensate in the Yang-Mills (paper IV). For Electroweak theory we derive the effective gauge-invariant Lagrangian by doing the Kaluza-Klein reduction of higher-dimensional gravity with 3-brane, thus making explicit the geometric interpretation for gauge-invariant supercurrents. The analogy is then made more precise in the framework of exact supergravity solutions. Thus, we interpret the Higgs effect as spontaneous breaking of Kaluza-Klein gauge symmetry and this leads to interpretation of Higgs field as a dilaton (papers I and II).

In Part II of the thesis we study rather simple field theories, called “geometric” or “instantonic”. Their defining property is exact localization on finite-dimensional spaces – the moduli spaces of instantons. These theories allow to account exactly for non-linearity of space of fields, in this respect they go beyond the standard Gaussian perturbation theory.

In paper V we show how to construct a geometric theory of chiral boson by embedding it into the geometric field theory. In Paper VI we elaborate on the simplest geometric field theory – the supersymmetric Quantum Mechanics and construct new non-perturbative topological observables that have a transparent meaning both in geometric and in the Hamiltonian formalisms. In Paper VII we are motivated by making perturbations away from the simple instantonic limit. For that we need to carefully define the observables that are quadratic in momenta and develop the way to compute them in geometric framework. These correspond geometrically to bivector fields (or, in general, the polyvector fields). We investigate the local limit of polyvector fields and compare the geometric calculation with free-field approach.

Place, publisher, year, edition, pages
Uppsala: Uppsala University, 2010. 93 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 761
Yang-Mills theory, spin-charge separation, Kaluza-Klein theory, branes, curved beta-gamma systems
National Category
Other Physics Topics
Research subject
Theoretical Physics
urn:nbn:se:uu:diva-129670 (URN)978-91-554-7873-5 (ISBN)
Public defence
2010-10-11, Häggsalen, Ångström lab, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Available from: 2010-09-16 Created: 2010-08-22 Last updated: 2011-03-08

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