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RISS 인기검색어
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- 저자 : Emirdag, Pinar (검색결과 1 건)
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Numerical calculations of quantum field theories on the continuum
Emirdag, Pinar Brown University 2002 해외박사(DDOD)
Source Galerkin technique is an alternative numerical method developed by Garcìa, Guralnik, and Lawson at Brown. It is not based on any statistical methods and has controllable errors. It also has the advantage that it can be used in a continuum formulation. This new method promises an increase in accuracy and speed of calculations. In this method, we treat field theory with the presence of external sources. The functional relations become a set of coupled differential equations for the generating functional <italic>Z</italic>. Source Galerkin is used to solve these equations for the Green's functions of the theory. According to this technique, the set of the residuals and the test functions are required to be orthogonal with respect to some inner product. The test functions that we are using are polynomials that consists of source terms and preserve the group symmetry of the problem. Symmetries of translation and reflection invariance are used in constructing the solution. A good choice of the test functions and the initial guess speeds the convergence to the result. The accuracy of the approximation can be judged by measuring its numerical stability and convergence. An exact solution can be obtained as the number of test functions increases. This sort of techniques for solving sets of differential equations are known as Galerkin methods. Application of this method to various field theories are investigated. Quantities such as mass gap and β function are calculated. The results are compared to the results in the literature.
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