Automated computation of one-loop integrals in massless theories

We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory, and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization.Received: 21 February 2005, Revised: 31 March 2005, Published online: 13 May 2005     

Anatomy of one-loop effective action in non-commutative scalar field theories

The one-loop effective action of non-commutative scalar field theory with cubic self-interaction is studied. Utilizing the worldline formulation, both the planar and non-planar parts of the effective action are computed explicitly. We find complete agreement of the result with the Seiberg–Witten limit of a string worldsheet computation and with the standard Feynman diagrammatics. We prove that, in the low-energy and large non-commutativity limit, the non-planar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators. Received: 22 July 2001 / Revised version: 19 October 2001 / Published online: 7 December 2001     

Quadratic and quartic one-loop divergences in gauge theories and their cancellation in supergravity

The quadratic and quartic divergences cancel in N = 2 supergravity in photon-photon scattering. They are defined by modified dimensional regularization as the residues of poles at d = 2 and d = 0 dimensions, respectively. Other definitions are shown to violate general coordinate invariance and Yang-Mills invariance. 't Hooft's algorithm for the one-loop divergences is extended to the case of higher-order divergences.     

Large-mass expansions or one-loop effective actions and fermion currents

The large-mass expansion of the functional determinants for second-order elliptic operators and general Dirac operators is calculated for four-dimensional flat euclidean space using zeta function regularisation and heat kernel methods. The results are applicable to one-loop boson and fermion effective actions. In addition the expansions of covariantly regularised fermion currents are derived. It is also possible for the corresponding Pauli-Villars regularised forms to be then simply obtained and the modified currents then reproduce the usual Bardeen anomaly. Although covariant methods are used it is shown how to derive the expansion for the phase of the fermion determinant, which is non-covariant and produces the anomaly, in terms of a representation as a five-dimensional integral which is related to the spectral asymmetry for a suitable spinor hamiltonian. This relation is essentially exact and is demonstrated by considering the variation of the phase with respect to the Dirac operator.     

Surface integrals and monopole charges in non-abelian gauge theories

We derive a formula which gives all the magnetic charges (topological invariants) of a monopole in the adjoint representation of a non-abelian gauge theory in terms of surface integrals at infinity.Supported in part by the National Science Foundation under Grant No. PHY 79-16812Junior Fellow, Harvard University Society of Fellows     

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.     

Three- and four-nucleon systems from chiral effective field theory

Recently developed chiral nucleon-nucleon (NN) forces at next-to-leading order (NLO), that describe NN phase shifts up to about 100 MeV fairly well, have been applied to 3N and 4N systems. Faddeev-Yakubovsky equations have been solved rigorously. The resulting 3N and 4N binding energies are in the same range as found using standard NN potentials. In addition, low-energy 3N scattering observables are very well reproduced as for standard NN forces. The long-standing A(y) puzzle is absent at NLO. The cutoff dependence of the scattering observables is rather weak.     

The graviton one-loop effective action in cosmological space-times with constant deceleration

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant . After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one-loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in Janssen et al. (2008) [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of and shows no secular growth.     

Calculation of the one-loop effective potential in induced two-dimensional quantum gravitation

The one-loop effective potential is calculated in induced two-dimensional quantum gravitation. There are no quantum corrections to the classical potential in the Jackiw-Teitelboim exactly solvable model. This fact is in agreement with the results of a nonperturbation analysis.Leninskii Komsomol Education Institute, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 69–72, June, 1992.     

Scalar parameters in effective gauge theories

We apply Weinberg's method of effective gauge theories to the study of light scalar masses and coupling constants, in a simplified model with two widely separated mass scales. No improvement of the unnaturalness in the Higgs sector is seen.