In 1962 Stanley Mandelstam proposed a new formalism for electrodynamics and gravitation1 with wave functions (fields) depending on paths rather than spacetime points. In 1968 he extended this path-dependent formalism to the gauge theories.2 In the last decade this approach, whose advantage is complete gauge invariance, has been considerably developed in different directions. Wu and Yang showed3 that so-called nonintegrable phase factors arising from the path-dependent approach, represent an electro-magnetic or gauge field more adequately than the field strength does. Many other authors4,5,6 have exploited the path-dependent or contour formalism in the gauge theory. Some new ideas (for example concerning phases of gauge fields and confinement of quarks) were connected essentially with the contour formalism.5 But application of the path-dependent approach to gravitation was almost never discussed in literature.
KeywordsGauge Theory Minkowski Space Gauge Field Lorentz Group Curve Spacetime
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