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|Title||Hamilton-Jacobi Treatment of Fields with Constraints|
In this thesis the basic formalism for treating constrained Hamiltonian systems of field theory are discussed within the framework of two methods, Dirac's and Hamilton-Jacobi method. Lagrangian for a fermionic and a scalar field, the scalar field coupled to two flavours of fermions through Yukawa couplings and non-Abelian theory of fermions interacting with gauge bosons as an application of non-Abelian Yang-Mills theories are treated as constrained systems using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. These equations of motion are in exact agreement with those equations that had been obtained using Dirac's method. Path integral quantization of the coupled scalar field minimally to the vector potential, is discussed as an application of field theory containing first-class constraints only, and the quantization of the relativistic local free field with linear velocity of dimension D containing both first and second-class constraints. Also Hamilton-Jacobi quantization of electromagnetic field coupled to a spinor is studied.
|Publisher||the islamic university|
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