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Giampiero Esposito

Publications and source records attributed to Giampiero Esposito.

At least 145 records · Page 8Linked to original sources
arXiv2003

On the photon Green functions in curved space-time

Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Gamma functions. Eventually, the full asymptotic expansion of the Feynman photon Green function at small values of the world function, as well as its explicit dependence on the gauge parameter, are obtained without adding by hand a mass term to the Faddeev--Popov Lagrangian. Coincidence limits of second covariant derivatives of the associated Hadamard function are also evaluated, as a first step towards the energy-momentum tensor in the non-minimal case.

hep-th↗
arXiv2003

Classical brackets for dissipative systems

We show how to write a set of brackets for the Langevin equation, describing the dissipative motion of a classical particle, subject to external random forces. The method does not rely on an action principle, and is based solely on the phenomenological description of the dissipative dynamics as given by the Langevin equation. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism.

hep-th↗
arXiv2003

Euclidean Quantum Gravity in Light of Spectral Geometry

A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral geometry, i.e. heat-kernel asymptotics for the Laplacian in the presence of Dirichlet, or Robin, or mixed boundary conditions; completely gauge-invariant boundary conditions in Euclidean quantum gravity; local vs. non-local boundary-value problems in one-loop Euclidean quantum theory via path integrals.

hep-th↗
arXiv2003

Spacetime Noncommutativity and Antisymmetric Tensor Dynamics in the Early Universe

This paper investigates the possible cosmological implications of the presence of an antisymmetric tensor field related to a lack of commutatitivity of spacetime coordinates at the Planck era. For this purpose, such a field is promoted to a dynamical variable, inspired by tensor formalism. By working to quadratic order in the antisymmetric tensor, we study the field equations in a Bianchi I universe in two models: an antisymmetric tensor plus scalar field coupled to gravity, or a cosmological constant and a free massless antisymmetric tensor. In the first scenario, numerical integration shows that, in the very early universe, the effects of the antisymmetric tensor can prevail on the scalar field, while at late times the former approaches zero and the latter drives the isotropization of the universe. In the second model, an approximate solution is obtained of a nonlinear ordinary differential equation which shows how the mean Hubble parameter and the difference between longitudinal and orthogonal Hubble parameter evolve in the early universe.

gr-qc↗
arXiv2003

On the occurrence of mass in field theory

This paper proves that it is possible to build a Lagrangian for quantum electrodynamics which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. Gauge independence is achieved upon considering the joint effect of gauge-averaging term and ghost fields. It remains possible to obtain a counterterm Lagrangian where the only non-gauge-invariant term is proportional to the squared divergence of the potential, while the photon propagator in momentum space falls off like 1 over (k-squared) at large k, which indeed agrees with perturbative renormalizability. The resulting radiative corrections to the Coulomb potential in QED are also shown to be gauge-independent. The experience acquired with quantum electrodynamics is used to investigate properties and problems of the extension of such ideas to non-Abelian gauge theories.

hep-th↗
arXiv2003

On the behaviour of a rigid Casimir cavity in a gravitational field

A detailed investigation is presented of the energy-momentum tensor approach to the evaluation of the force acting on a rigid Casimir cavity in a weak gravitational field. Such a force turns out to have opposite direction with respect to the gravitational acceleration. The order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.

hep-th↗
arXiv2003

Peierls Brackets in Field Theory

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.

hep-th↗
arXiv2002

Peierls Brackets in Theoretical Physics

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to field theory and point Lagrangians.

hep-th↗
arXiv2002

Chiral bag boundary conditions on the ball

Local boundary conditions for spinor fields are expressed in terms of a 1-parameter family of boundary operators, and find applications ranging from (supersymmetric) quantum cosmology to the bag model in quantum chromodynamics. The present paper proves that, for massless spinor fields on the Euclidean ball in dimensions d=2,4,6, the resulting zeta(0) value is independent of such a theta parameter, while the various heat-kernel coefficients exhibit a theta-dependence which is eventually expressed in a simple way through hyperbolic functions and their integer powers.

hep-th↗
arXiv2002

Vacuum fluctuation force on a rigid Casimir cavity in a gravitational field

We discuss the possibility of verifying the equivalence principle for the zero-point energy of quantum electrodynamics, by evaluating the force, produced by vacuum fluctuations, acting on a rigid Casimir cavity in a weak gravitational field. The resulting force has opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.

quant-ph↗
arXiv2002

On the Riemann Function and Irregular Singular Points for Axisymmetric Black Hole Collisions at the Speed of Light

The news function providing some relevant information about angular distribution of gravitational radiation in axisymmetric black hole collisions at the speed of light had been evaluated in the literature by perturbation methods, after inverting second-order hyperbolic operators with variable coefficients in two independent variables. More recent work has related the appropriate Green function to the Riemann function for such a class of hyperbolic operators in two variables. The present paper obtains an improvement in the evaluation of the coefficients occurring in the second-order equation obeyed by the Riemann function, which might prove useful for numerical purposes. Eventually, we find under which conditions the original Green-function calculation reduces to finding solutions of an inhomogeneous second-order ordinary differential equation with a non-regular singular point.

gr-qc↗
arXiv2001

Towards a Spectral Proof of the Mass Gap in QCD?

Yang--Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The operator P is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of P are evaluated as a first step towards the more difficult problems of quantized Yang--Mills theory.

hep-th↗
arXiv2001

A new application of non-canonical maps in quantum mechanics

A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped into new operators, not conjugate to each other, whose standard commutator equals the identity plus a correction proportional to the original number operator. The consistency condition for the existence of this new set of operators is derived, by exploiting the Stone theorem on 1-parameter unitary groups. The above scheme leads to modified equations of motion which do not preserve the properties of the original first-order set for annihilation and creation operators. Their relation with commutation relations is also studied.

quant-ph↗
arXiv2001

Gravitational effects on a rigid Casimir cavity

Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a weak gravitational field. Such a force is here evaluated and is found to have opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is analyzed and experimental detection is discussed, bearing in mind the current technological resources.

quant-ph↗
arXiv2000

Essential self-adjointness in one-loop quantum cosmology

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.

gr-qc↗
arXiv2000

The Role of Elliptic Operators in the Initial-Value Problem for General Relativity

The Arnowitt-Deser-Misner (ADM) equations are deeply intertwined with discrete spectral resolutions of an elliptic operator of Laplace type associated with the spacelike hypersurfaces which foliate the space-time manifold, and the non-linearities of the four-dimensional hyperbolic theory are mapped into the potential term occurring in this operator. The ADM equations are here re-expressed as a coupled first-order system for the induced metric and the trace-free part of the extrinsic-curvature tensor, and their formulation in terms of integral equations is studied.

gr-qc↗
arXiv2000

Dirac Operator and Spectral Geometry

This paper is devoted to mathematical and physical properties of the Dirac operator and spectral geometry. Spin-structures in Lorentzian and Riemannian manifolds, and the global theory of the Dirac operator, are first analyzed. Elliptic boundary-value problems, index problems for closed manifolds and for manifolds with boundary, Bott periodicity and K-theory are then presented. This makes it clear why the Dirac operator is the most fundamental, in the theory of elliptic operators on manifolds. The topic of spectral geometry is developed by studying non-local boundary conditions of the Atiyah-Patodi-Singer type, and heat-kernel asymptotics for operators of Laplace type on manifolds with boundary. The emphasis is put on the functorial method, which studies the behaviour of differential operators, boundary operators and heat-kernel coefficients under conformal rescalings of the background metric. In the second part, a number of relevant physical applications are studied: non-local boundary conditions for massless spin-1/2 fields, massless spin-3/2 potentials on manifolds with boundary, geometric theory of massive spin-3/2 potentials, local boundary conditions in quantum supergravity, quark boundary conditions, one-loop quantum cosmology, conformally covariant operators and Euclidean quantum gravity.

hep-th↗