On Using the Quantum Mechanical Path Integral in Quantum Field Theory

✍ Scribed by D.G.C. Mckeon

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 372 KB
• Volume: 224
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1993.1042

✦ Synopsis

It is shown how matrix elements of the form (\left\langle x\left|e^{-i f t}\right| y\right\rangle), which arise in closed-form expressions for the generating functional, can be evaluated perturbatively using a path integral encountered in the quantum mechanics of a single particle. This allows one to compute Green's functions without ever having to evaluate loop-momentum integrals. This technique is illustrated by considering, in the context of operator regularization, the vacuum polarization in scalar and spinor electrodynamics to one-loop order, the two-point function in (\phi_{0}^{?}) theory to two-loop order, the spinor self-energy in massless electrodynamics to one-loop order, the two-point function in Yang-Mills theory to one-loop order and the three-point function in axial electrodynamics to one-loop order. ' 1993 Academic Press. Inc.