By V. Parameswaran Nair

ISBN-10: 0387213864

ISBN-13: 9780387213866

Based on lecture notes for a graduate direction given for a few years on the urban collage of recent York. at this time, there's no

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Fujikawa, Int. J. Mod. Phys. A16, 4025 (2001). 8. For the canonical procedure on symmetrization of energy-momentum tensor, see F. Belinfante, Physica 6, 887 (1939); ibid. 7, 305 (1940). The symmetric energy-momentum tensor via variation of the metric is discussed in many books on relativity, for example, S. Weinberg, Gravitation and Cosmology, Wiley Text Books (1972); L. M. Lifshitz, Classical Theory of Fields, Butterworth-Heinemann, 4th edition (1980). 9. The classical conformal invariance of Maxwell equations goes back to E.

23) aI ≡ δξ I = {ξ I , G} In fact, this equation may be taken as the deﬁnition of the generator. , Poisson brackets with G, are canonical. 25) These equations show why Poisson brackets are important. The change of any variable, so long as it is canonical, is given by the Poisson bracket of the variable with the generating function for the transformation. We now ﬁnd the generators of some important canonical transformations. 1. Change of ϕr (x). 26) V 2. Change of πr (x). 27) V 3. Space translations.

Lond. Math. Soc. 8, 223 (1910). 1 Scalar ﬁeld propagators As a prelude to the discussion of interactions we calculate commutators and propagators. Consider the theory of the scalar ﬁeld ﬁrst. 2) k2 + m2 ). 3) in the limit V → ∞. We can rewrite this as [φ(x), φ(y)] = C d4 k (2π)4 k2 −i − m2 e−ik(x−y) ≡ ∆(x, y) where the contour is shown below. ✬ ✛ . -ω ✫✲ ✩ . 1. 4) is to be interpreted as follows. We carry out the k0 -integration ﬁrst, as a contour integral in the complex k0 -plane, along the contour shown.

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