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# The Functional Measure In Quantum Field Theory

## Abstract

One of the great legacies left to the physics community by Albert Einstein is the idea that physical predictions should be independent of the choice of coordinates. A natural way to ensure this is to formulate a theory in a way which is manifestly covariant. This is what is done for instance in the general theory of relativity. Today most physicists would not even contemplate founding a theory based on a preferred coordinate system or frame. The lack of a preferential frame is often exploited in calculations since, for example, derivations of certain results are often simpler if one adopts a coordinate system suitable for the symmetries of the problem. In general relativity it is often convenient to use a local orthonormal frame in which the metric tensor becomes just that for flat spacetime. One of the main purposes of this talk is to discuss how these ideas carry over into quantum field theory, particularly in relation to the functional measure.

## Keywords

Quantum Gravity Configuration Space Curve Spacetime Functional Measure Conformal Anomaly## Preview

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## REFERENCES

- K. Fujikawa, Path-integral measure for gauge-invariant fermion theories, Phys. Rev. Lett. 42 : 1195 (1979).ADSCrossRefGoogle Scholar
- K. Fujikawa, Comment on chiral and conformal anomalies, Phys. Rev. Lett 44: 1733 (1980).MathSciNetADSCrossRefGoogle Scholar
- K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21 : 2848 (1980).MathSciNetADSCrossRefGoogle Scholar
- K. Fujikawa, Energy-momentum tensor in quantum field theory, Phys. Rev. D 23 : 2262 (1981).MathSciNetADSCrossRefGoogle Scholar
- K. Fujikawa, Path integral measure for gravitational interactions, Nucl. Phys. B226 : 437 (1983).ADSCrossRefGoogle Scholar
- 6.K. Fujikawa, Path integral quantization of gravitational interactions - local symmetry properties, in: “Quantum Gravity and Cosmology”, H. Sato, T. Inami, ed., World Scientific, Singapore (1986). Google Scholar
- 7.A. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. 103B : 207 (1981). MathSciNetADSGoogle Scholar
- 8.A, Polyakov, Quantum geometry of fermionic strings, Phys. Lett. 130B : 211 (1981). MathSciNetADSGoogle Scholar
- 9.R.K. Unz, Path integration and the functional measure, SLAC-PUB-3 656, unpublished (1985).Google Scholar
- R.K. Unz, The functional measure in Kaluza-Klein theories, Phys. Rev. D 32 : 2539 (1985).MathSciNetADSCrossRefGoogle Scholar
- 11.D.J. Toms, The functional measure for quantum field theory in curved spacetime, University of Newcastle upon Tyne report NCL 86 -TP (1986). Google Scholar
- 12.B.S. DeWitt, Quantum gravity: the new synthesis, in: “General Relativity”, S.W. Hawking, W. Israel, ed., Cambridge University Press, Cambridge (1979). Google Scholar
- 13.B.S. DeWitt, Covariant quantum geometrodynamics, in “Magic Without Magic”, J. Klauder, ed., W.H. Freeman, San Francisco (1972). Google Scholar
- R.P. Feynman, An operator calculus having applications in quantum electrodynamics, Phys. Rev. 84 : 108 (1951).MathSciNetADSMATHCrossRefGoogle Scholar
- S.A. Fulling, Ph.D. Thesis, Princeton University, unpublished (1972).Google Scholar
- 16.G. Vilkovisky, The gospel according to DeWitt, in “Quantum Theory of Gravity”, S.M. Christensen, ed., Adam Hilger, Bristol (1984). Google Scholar
- 17.B.S. DeWitt, Quantum theory of gravity. I. The canonical theory, Phys. Rev. 160 : 1113 (1967). ADSCrossRefGoogle Scholar