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Non-Perturbative Analysis of Some Simple Field Theories on a Momentum Space Lattice


Brooks, Eugene David, III (1984) Non-Perturbative Analysis of Some Simple Field Theories on a Momentum Space Lattice. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/333S-XC47.


In this work, we develop a new technique for the numerical study of quantum field theory. The procedure, borrowed from non-relativistic quantum mechanics, is that of finding the eigenvalues of a finite Hamiltonian matrix. The matrix is created by evaluating the matrix elements of the Hamiltonian operator on a finite basis of states. The eigenvalues and eigenvectors of the finite dimensional matrix become an accurate approximation to those of the physical system as the finite basis of states is extended to become more complete.

We study a model of scalars coupled to fermions in 0+1 dimensions as a simple field theory to consider in the course of developing the technique. We find in the course of studying this model a change of basis which diagonalizes the Hamiltonian in the large coupling limit. The importance of this transformation is that it can be generalized to higher dimensional field theories involving a trilinear coupling between a Bose and a Fermi field.

Having developed the numerical and analytical techniques, we consider a Fermi field coupled to a Bose field in 1+1 dimensions with the Yukawa coupling λΨΨΨ. We extend the large coupling limit basis of the 0+1 dimensional model to this case using a Bogoliubov transformation on the fermions. Although we do not use this basis in the numerical work due to its complexity, it provides a handle on the behavior of the system in the large coupling limit. In this model we consider the effects of renormalization and the generation of bound states.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bridges, William B.
Thesis Committee:
  • Bridges, William B. (chair)
  • Cowan, Eugene W.
  • George, Nicholas A.
  • Papas, Charles Herach
  • Psaltis, Demetri
Defense Date:10 October 1983
Non-Caltech Author Email:brooks3 (AT)
Record Number:CaltechETD:etd-04132005-100141
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1371
Deposited By: Imported from ETD-db
Deposited On:13 Apr 2005
Last Modified:22 Sep 2020 22:46

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PDF (Brooks_ed_1984.pdf) - Final Version
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