# Finite Element Approximation in Quantum Theory

• Carl M. Bender
Part of the Progress in Physics book series (PMP, volume 8)

## Abstract

Many of the approaches to numerical quantum field theory which have been developed to date start from the Euclidean path integral formulation of the theory. This is because it is possible, using path integrals, to write closed form, albeit formal and difficult to evaluate, expressions for the quantities of physical interest, namely the Green’s functions. Thus, in this approach, the focus is not on finding the direct solution to the equations of quantum field theory, but rather on developing an effective and reliable method for evaluating the functional integrals representing the Green’s functions.

## Keywords

Finite Element Method Small Eigenvalue Finite Element Approximation Exact Answer Heisenberg Equation
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## References

1. [1]
This work was done in collaboration with D. H. Sharp. See C. M. Bender and 0. H. Sharp, Phys. Rev. Lett. 50, 1535 (1983).
2. [2]
Useful general references on the finite element method are G. Strang and G. J. Fix, An Analysis of The Finite Element Hethod. (Prentice-Hall Inc., Englewood Cliffs, 1973 ) and T.J. Chung, Finite Element Analysis in Fluid Dynamics, ( McGraw-HiII, New York, 19780 )Google Scholar
3. [3]
There are several Interesting remarks to be made here. One intriguing question is whether (12) and (13) might be used in coronation with [q0P0]= i to find a spectrun 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. [4]
The matrix S is a nunerical matrix containing the lattice spacings h and k. It is symmetric because with properly chosen boundary conditions the operator 7Z in the continuum is symmetric.Google Scholar