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Path Integration and the Functional Measure PDF - Previous Volume / Next Volume
by R.K. Unz
In Il Nuovo Cimento, October 1985, pp. 397-426

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IL NUOVO CIMENTO VOL. 92 A, N. 4 21 Aprile 1986
Path Integration and the Functional Measure C **
B. K. UNZ ***
Department of Physics, Stanford University - Stanford, CA. 94305
Stan/rod Linear Accelerator Center, Stanford University - Stanford, CA. 94305
ricevuto ii 31 Ottobre 1985
Summary. - The functional measure for the Feynman path integral
is investigated, and it is argued that nontrivial measure factors should
not be automatically discarded as is often done. The fundamental hypoth
esis of path integration is stated in its Hamiltonian formulation and is
used, together with the Faddeev-Popov ansatz, to derive the general
form of the canonical functional measure for all gauged or ungauged
theories of integer spin fields in any number of space-time dimensions.
This general result is then used to calculate the effective functional meas
ures for scalar, vector, and gravitational fields in more than two dimen
sions at energies low compared to the Planck mass. It is shown that these
results indicate the self-consistency and plausibility of the canonical func
tional measure over other functional measures and suggest an important
relationship between bosonic and fermionic degrees of fieedom. The
canonical functional measure factors associated with fields of half-integer
spin and with auxiliary fields are also derived.
PACS. 11.10. - Field theory.
1. - Introduction.
The path integral formulation of quantum field theory, developed by
FEYNMAN, has been responsible for many of the most important develop
* To speed up publication, the author of this paper has agreed to not receive the
proofs for correction.
Work supported by the Department of Energy, contract DE-ACO3-76SF00515.
*** National Science Foundation Graduate Fellow.
397


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