بررسي تقارن هاي ريسمان پولياكوف در فرمول بندي هاميلتوني

چكيده انگليسي :

The Study of Non adiabatic Perturbations of the Vector Fields at the End of Inflation by Numerical Methods Leila Heydari l heidari@ph iut ac ir 3 3 2012 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Persian Supervisor Dr A Shirzad Shirzad@cc iut ac ir Abstract Symmetries play essential role in theoretical physics A transformation is said to be symmetry if the action remains unchanged under certain variations of the variables It can be shown that for regu lar Lagrangians symmetry transformations can be derived from the corresponding generators in the Hamiltonian formulation which are constants of motion as well One can investigate the properties of the symmetry by studying the algebra of the generators in the canonical formulation This point is more essential in the quantum theory where the physical states should be classified in representations of the canonical algebra of generators of the symmetry transformation A large class of symmetry transformations is the set of gauge transformations Gauge theories are of the most interest for physi cists in the recent decades A system is said to possess gauge symmetry if the action as well as the equations of motion do not change under transformations which include arbitrary functions of time and a the set its derivatives up to a finite order From the canonical viewpoint one needs to find the generators of the gauge symmetry and their algebra in order to study the effect of that symmetry on the physical variables For gauge theories we know from the Dirac conjecture that all of the first class constraints both primary and secondary ones are generators of the gauge transformations However it is not an easy task in the general case to construct the most general form of the gauge generating function as an expansion over first class constraints and or the derivatives of the arbitrary functions The problem is more critical for general covariant theories such as Hilbert Einstein action and the Polyakov string In the recent years so many general covariant models in different dimensions have been proposed such as the topological massive gravity Hojava gravity and so on As we know the most important symmetry of these models is the invariance of the action under arbitrary change of the variables describing the space time manifold which is called reparameterization invariance by physicists or diffeomorphysm in the language of mathematicians Hence the main problem is to find the relationship between the constraints of the system at the Hamiltonian level and the repa rameterization which is the gauge symmetry of the system at the Lagrangian level In this thesis we have tried to find the generating function of gauge symmetries of the Polyakov string which includes the Weyl transformation as well For this reason we have derived first the constraint structure of the system in some appropriate variables and then we have derived the variations of these variables under reparameterizations as well as Weyl transformations We have used the Pons approach 9 after ward to write down the generating function of the symmetries We show that this generating function works perfectly in the sense that all of the required transformations are derived under finding the FL projection of the Poisson brackets of the corresponding variable with the generating function with additional terms coming from non projectablity of the corresponding transformation as described in the text Keywords Gauge theories Generating function of Gauge transformations Polyakov string Reparameterization

حيدري، ليلا

بررسي تقارن هاي ريسمان پولياكوف در فرمول بندي هاميلتوني

نظريه هاي پيمانه اي , تابع مولد , تبديلات پيمانه اي , وردش كنش - كل