Related papers: Coordinate-invariant Path Integral Methods in Conf…
Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in-in formalism, which requires only…
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…
We study noncommutative field theories, which are inherently nonlocal, using a Poincar\'e-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features…
A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2\pi\hbar/T$, where $T$ is the typical…
It has long been demonstrated that the vacuum scalar-tensor theory in the Jordan-frame Brans-Dicke parametrization is form-invariant under conformal transformations, provided that a suitable transformation of the coupling parameter $\omega$…
In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With…
We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective…
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…
In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the…
The diagrammatic computation of the chiral anomaly is associated with momentum-routing invariance breaking. This happens because the momentum routing in the internal lines of a loop diagram is chosen such that the gauge Ward identities hold…
The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Amongst these are transport…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral…
Power duality in Feynman's path integral formulation of quantum mechanics is investigated. The power duality transformation consists of a change in coordinate and time variables, an exchange of energy and coupling, and a classical angular…
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of…
When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the…
We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a…