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Project List » GEOMETRICAL METHODS IN QUANTUM MECHANICS AND QUANTUM FIELD THEORY

GEOMETRICAL METHODS IN QUANTUM MECHANICS AND QUANTUM FIELD THEORY
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Acronym: MGMCC
Contracting Authority: Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI)
Number / Date of the contract: 454 / 15.01.2009
Idei
Project Manager: Stefan Alexandru Adrian Berceanu
Partners: INSTITUTE OF MATHEMATICS "SIMION STOILOW"OF THE ROMANIAN ACADEMY
Starting date / finishing date: 2009-01-01 / 2011-12-31
Project value: 1000000 RON
Abstract: THE QUANTUM THEORY OF GRAVITY CAN BE STUDIED IN THE FRAMEWORK OF PERTURBATIVE RENORMALIZATION THEORY; IN THIS FRAMEWORK ONE STUDIES IN FACT A THEORY OF INTERACTIONS OF QUANTUM PARTICLES OF NULL MASS AND HELICITY 2. SUCH A THEORY IS IN FACT A GAUGE THEORY SIMILAR TO YANG-MILLS MODELS AND AN IMPORTANT PROBLEM IS TO PROVE GAUGE INVARIANCE OF THE CHRONOLOGICAL PRODUCT IN ALL ORDERS OF PERTURBATION THEORY. FOLLOWING THESE IDEAS THE PROJECT WILL TRY TO CLARIFY THE RENORMALIZABILITY PROPERTY AT LEAST IN THE SECOND ORDER OF THE PERTURBATION THEORY. ON THE OTHER HAND, THE PROJECT DEALS WITH NON-COMMUTATIVE QUANTUM FIELD THEORY. WE WILL PROPOSE A RENORMALIZABLE SCALAR MODEL ON THE MOYAL SPACE. THIS MODEL WILL FURTHERMORE BE TRANSLATION-INVARIANT. FURTHERMORE, WE PROPOSE HERE TO STUDY THE COMMUTATIVE LIMIT OF SUCH A MODEL, THIS TOPIC BEING A CRUCIAL ONE FOR THE STUDY OF ALL KNOWN RENORMALIZABLE NON-COMMUTATIVE MODELS. THE BEST CANDIDATE FOR A UNIFIED THEORY OF ALL FUNDAMENTAL INTERACTIONS (GRAVITATIONAL, ELECTROMAGNETIC, WEAK AND STRONG) IS STRING THEORY. IN CONSEQUENCE, WE PROPOSE THE STUDY OF THE LOW ENERGY LIMIT OF STRING THEORY. SIMULTANEOUSLY, WE SHALL INVESTIGATE THE GEOMETRY OF THE MANIFOLDS ON WHICH THE COHERENT STATES ASSOCIATED TO THE JACOBI GROUP ARE BASED: THE KAEHLER TWO-FORM, THE REPRODUCING KERNEL, THE BASE OF FUNCTIONS OF THE HILBERT SPACE.

Objectives:

THE STAGES OF THE PROJECT AND DELIVERY DATES
1. The renormalization of the quantum gravity on the linear approximation  (2009-09-10)
2. Proposition of a translation-invariant scalar model on the Moyal space.  (2009-11-30)
3. The commutative limit of the translation-invariant on the Moyal space.  (2010-10-30)
4. The investigation of some geometrical properties of the manifold on which the coherent states associated to the Jacobi group are defined; The study of instanton effects in orientifold models  (2011-10-30)
RESULTS
PUBLISHED ARTICLES
RESEARCH TEAM


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