Asymptotic Heat Kernels in Quantum Field Theory
نویسنده
چکیده
Asymptotic expansions were first introduced by Henri Poincaré in 1886. This paper describes their application to the semi-classical evaluation of amplitudes in quantum field theory with boundaries. By using zeta-function regularization, the conformal anomaly for a massless spin-12 field in flat Euclidean backgrounds with boundary is obtained on imposing locally supersymmetric boundary conditions. The quantization program for gauge fields and gravitation in the presence of boundaries is then introduced by focusing on conformal anomalies for higher-spin fields. The conditions under which the covariant Schwinger-DeWitt and the non-covariant, mode-by-mode analysis of quantum amplitudes agree are described. To appear in: Proceedings of the Henri Poincaré Conference, Protvino, June 1994.
منابع مشابه
Distributional Asymptotic Expansions of Spectral Functions and of the Associated Green Kernels
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and more precisely determined by means of tools from distribution theory and summability theory. (These are the same, insofar as recently the classic Cesàro–Riesz ...
متن کاملExamples of potentials with convergent Schwinger — DeWitt expansion
Convergence of the Schwinger — DeWitt expansion for the evolution operator kernel for special class of potentials is studied. It is shown, that this expansion, which is in general case asymptotic, converges for the potentials considered (widely used, in particular, in one-dimensional many-body problems), and besides, convergence takes place only for definite discrete values of the coupling cons...
متن کاملTopological Conformal Field Theories and Gauge Theories
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a bundle of Frobenius algebras, satisfying various conditions. These forms satisfy gluing conditions which mean they form an open topological conformal field th...
متن کاملX iv : h ep - t h / 96 08 11 5 v 1 1 7 A ug 1 99 6 The : φ 44 : quantum field theory , II . Integrability of Wick kernels . ∗
We continue the construction of the : φ 4 : quantum field theory. In this paper we consider the Wick kernel of the interacting quantum field. Using the Fock– Bargmann–Berezin–Segal integral representation we prove that this kernel defines a unique operator–valued generalized function on the space Sα(IR4) for any α < 6/5, i.e. the constructed quantum field is the generalized operator-valued func...
متن کاملOn the Large Time Behavior of Heat Kernels on Lie Groups
We prove Gaussian estimates for heat kernels on semisimple Lie groups by using the method of Bloch wave representation. We also give a large time asymptotic expansion for heat kernels on compact extensions of abelian Lie groups.
متن کامل