Worldline approach to vector and antisymmetric tensor fields

The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning particle coupled to spacetime gravity. The action has a local N=2 worldline supersymmetry with a gauged U(1) symmetry that includes a Chern-Simons coupling. Its quantization on the torus produces the one-loop effective action for a single antisymmetric tensor. We use this worldline representation to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side results we obtain the correct trace anomaly of a spin 1 particle in four dimensions as well as exact duality relations between differential form gauge fields. This approach yields a drastic simplification over standard heat-kernel methods. It contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Worldline methods are generically simpler and more efficient in perturbative computations then standard QFT Feynman rules. This is particularly evident when the coupling to gravity is considered.Comment: 30 pages, 5 figures, references adde

Coupling of Linearized Gravity to Nonrelativistic Test Particles: Dynamics in the General Laboratory Frame

The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of the couplings, and the known results of tidal effects on test particles according to classical general relativity are pointed out. As a step towards resolving these inconsistencies, a General Laboratory Frame fixed on the worldline of an observer is constructed. In this frame, the dynamics of nonrelativistic test particles in the linearized gravity limit is studied, and their Hamiltonian dynamics is derived. It is shown that for stationary metrics this Hamiltonian reduces to the usual Hamiltonian for nonrelativistic particles undergoing geodesic motion. For nonstationary metrics with long-wavelength gravitational waves (GWs) present, it reduces to the Hamiltonian for a nonrelativistic particle undergoing geodesic \textit{deviation} motion. Arbitrary-wavelength GWs couple to the test particle through a vector-potential-like field $N_a$, the net result of the tidal forces that the GW induces in the system, namely, a local velocity field on the system induced by tidal effects as seen by an observer in the general laboratory frame. Effective electric and magnetic fields, which are related to the electric and magnetic parts of the Weyl tensor, are constructed from $N_a$ that obey equations of the same form as Maxwell's equations . A gedankin gravitational Aharonov-Bohm-type experiment using $N_a$ to measure the interference of quantum test particles is presented.Comment: 38 pages, 7 figures, written in ReVTeX. To appear in Physical Review D. Galley proofs corrections adde

Gravity action on the rapidly varying metrics

We consider a four-dimensional simplicial complex and the minisuperspace general relativity system described by the metric flat in the most part of the interior of every 4-simplex with exception of a thin layer of thickness $\propto \varepsilon$ along the every three-dimensional face where the metric undergoes jump between the two 4-simplices sharing this face. At $\varepsilon \to 0$ this jump would become discontinuity. Since, however, discontinuity of the (induced on the face) metric is not allowed in general relativity, the terms in the Einstein action tending to infinity at $\varepsilon \to 0$ arise. In the path integral approach, these terms lead to the pre-exponent factor with \dfuns requiring that the induced on the faces metric be continuous, i. e. the 4-simplices fit on their common faces. The other part of the path integral measure corresponds to the action being the sum of independent terms over the 4-simplices. Therefore this part of the path integral measure is the product of independent measures over the 4-simplices. The result obtained is in accordance with our previous one obtained from the symmetry considerations.Comment: 10 page

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.Comment: 6 pages, REVTeX

A spinorial perspective on massless photons

We exploit the fact that, in Minkowski space-time, gamma matrices are possibly more fundamental than the metric to describe how gauge invariance at perturbative level enforces a Lagrangian for spinor electrodynamics with massless photons. The term quadratic in the potential arises naturally in the gauge-fixed Lagrangian but has vanishing coefficient.Comment: 5 pages, Plain Te

States and Boundary Terms: Subtleties of Lorentzian AdS/CFT

We complete the project of specifying the Lorentzian AdS/CFT correspondence and its approximation by bulk semi-classical methods begun by earlier authors. At the end, the Lorentzian treatment is self-contained and requires no analytic continuation from the Euclidean. The new features involve a careful study of boundary terms associated with an initial time $t_-$ and a final time $t_+$. These boundary terms are determined by a choice of quantum states. The main results in the semi-classical approximation are 1) The times $t_\pm$ may be finite, and need only label Cauchy surfaces respectively to the past and future of the points at which one wishes to obtain CFT correlators. Subject to this condition on $t_\pm$, we provide a bulk computation of CFT correlators that is manifestly independent of $t_\pm$. 2) As a result of (1), all CFT correlators can be expressed in terms of a path integral over regions of spacetime {\it outside} of any black hole horizons. 3) The details of the boundary terms at $t_\pm$ serve to guarrantee that, at leading order in this approximation, any CFT one-point function is given by a simple boundary value of the classical bulk solution at null infinity, $I$. This work is dedicated to the memory of Bryce S. DeWitt. The remarks in this paper largely study the relation of the AdS/CFT dictionary to the Schwinger variational principle, which the author first learned from DeWitt as a Ph.D. student.Comment: 31 pages, JHEP style, various typos correcte

Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a contour integral representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a $d$-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.Comment: 26 Pages, 1 Figur

Self-force via a Green's function decomposition

The gravitational field of a particle of small mass \mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(\mu). One part is an inhomogeneous field which, near the particle, looks like the \mu/r field distorted by the local Riemann tensor; it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term''; it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.Comment: PRD, in press. Enhanced emphasis on the equivalence principl

The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case

We study the renormalization of the nonlinear effective SU(2) Lagrangian up to $O(p^4)$ with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology, guarantee the gauge covariance and incooperate the Ward indentities in our calculations. The renormalization group equations of the effective couplings are derived and analyzed. We find that the difference between the results gotten from the direct method and the renormalization group equation method can be quite large when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs, numerical analysis is renew

The effective action and quantum gauge transformations

The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can be used for construction simple gauge generators. For example, for the Yang-Mills theory the classically invariant effective action is obtained, reproducing DeWitt's result. For rank one theories a natural generalization is proposed.Comment: Revtex, 11 pages; added reference