A Proposal for the Solution of Quantum Field Theory Problems Using a Finite-Element Approximation
We show that the method of finite elements reduces intractable quantum operator differential equations to completely solvable operator difference equations. Early work suggests that this approximation technique is extremely accurate and very well suited to algebraic manipulation on a computer.
KeywordsDirac Equation dIscrete Action Heisenberg Equation Equal Time Commutation Relation Fermion Doubling
Unable to display preview. Download preview PDF.
- 3.There are several interesting remarks to be made here. One intriguing question is whether (12) and (13) might be used in combination with [q0, p0] = i to find a spectrum generating algebra. Second, one may ask what happens when the equation y = g (x) has multiple roots; that is, what role is played by instantons In these lattice calculations?Google Scholar
- 4.The matrix S is a numerical matrix containing the lattice spacings h and k. It is symmetric because with properly chosen boundary conditions the operator ∇2 the continuum is symmetric.Google Scholar
- 5b.J. M. Rabin, Phys. Rev. D24, 3218 (1981).Google Scholar
- 6.By experimenting with various types of difference schemes, R. Stacey independently discovered the dispersion relation (42) and the Kogut-Susklnd version of (41). See Phys. Rev. D26, 468 (1982).Google Scholar