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Finn Ravndal

Publications and source records attributed to Finn Ravndal.

33 records · Page 2Linked to original sources
arXiv2000

Problems with the Casimir Vacuum Energy

A critical look is taken at the calculation of the Casimir effect. The boundary conditions play an important role and should be imposed in a physical way. An acceptable result for the vacuum energy is only obtained when different regularization schemes yield the same result. Radiative corrections to the Casimir force between two parallel plates due to electromagnetic vacuum fluctuations have been obtained both in full QED and in a low-energy, effective field theory with conflicting results. Including surface terms in the effective Lagrangian, the QED result can be understood. Finally, a problem with the electromagnetic vacuum energy on $S^3$ is pointed out and a solution suggested. The structure of higher order corrections to this result is discussed.

hep-ph↗
arXiv2000

Proton-Proton Fusion in Effective Field Theory

The rate for the fusion process $p + p \ra d + e^+ + ν_e$ is calculated using non-relativistic effective field theory. Including the four-nucleon derivative interaction, results are obtained in next-to-leading order in the momentum expansion. This reproduces the effects of the effective range parameter. Coulomb interactions between the incoming protons are included non-perturbatively in a systematic way. The resulting fusion rate is independent of specific models and wavefunctions for the interacting nucleons. At this order in the effective Lagrangian there is an unknown counterterm which limits the numerical accuracy of the calculated rate given by the squared reduced matrix element $Λ^2(0) = 7.37$. Assuming the counterterm to have a natural magnitude, we estimate the accuracy of this result to be 6\% - 8\%. This is consistent with previous nuclear physics calculations based on effective range theory and inclusion of axial two-body weak currents. The true magnitude of the counterterm can be determined from a precise measurement of the cross-section for low-energy neutrino scattering on deuterons.

nucl-th↗
arXiv1999

Effective-Range Corrections to the Proton-Proton Fusion Rate

Proton-proton fusion is considered in the effective field theory of Kaplan, Savage and Wise. Coulomb effects are included systematically in a non-perturbative way. Including the dimension-eight derivative coupling which determines the effective ranges of the scattering amplitudes, next-to-leading order corrections to the fusion rate are calculated. When the renormalization mass is well above the characteristic energies of the system, this contribution gives a rate which is eight percent below the standard value. The difference can be due to an unknown counterterm which comes in at this order.

nucl-th↗
arXiv1999

Relativistic corrections to the Pionium Lifetime

Next to leading order contributions to the pionium lifetime are considered within non-relativistic effective field theory. A more precise determination of the coupling constants is then needed in order to be consistent with the relativistic pion-pion scattering amplitude which can be obtained from chiral perturbation theory. The relativistic correction is found to be 4.1% and corresponds simply to a more accurate value for the non-relativistic decay momentum.

hep-ph↗
arXiv1999

Coulomb Effects in Low Energy Proton-Proton Scattering

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate non-perturbatively Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in the PDS regularization scheme, we recover a modified form of the Blatt-Jackson relation between the scattering lengths. The effective range receives no corrections from the Coulomb interactions to this order. Also the case of scattering in channels where the Coulomb force is attractive, is considered. This is of importance for hadronic atoms.

hep-ph↗
arXiv1999

Proton-Proton Scattering Lengths from Effective Field Theory

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate the Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in PDS regularization scheme, we obtain a modified Jackson-Blatt relation for the scattering lengths which is found to be phenomenologically satisfactory. The effective range is not modified by Coulomb effects to this order in the calculation.

nucl-th↗
arXiv1999

Proton-Proton Fusion in Leading Order of Effective Field Theory

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate the rate for the fusion process $p + p \ra d + e^+ + ν_e$ to leading order in the momentum expansion. Coulomb effects are included non-perturbatively in a systematic way. The resulting rate is independent of specific models for the strong interactions at short distances and is in agreement with the standard result in the zero-range approximation.

nucl-th↗
arXiv1998

Non-Relativistic Pion Interactions and the Pionium Lifetime

We construct an effective Lagrangian for interacting pions with non-relativistic energies. The coupling constants can be expressed in terms of the different scattering lengths and slopes. When used in the calculation of the pionium decay rate, the scattering slope contribution gives a correction of about 8% compared with the lowest order contribution coming from the scattering lengths alone.

hep-ph↗
arXiv1998

Higher Order Hadronic Energy Level Shifts in Protonium

Using effective field theory for a proton and antiproton bound in a Coulomb potential, the shift of the ground state energy level is calculated to arbitrary order in the scattering length. Including the next order contact interaction, the correction due to the effective range parameter can also be obtained.

nucl-th↗
arXiv1998

Quantum Corrections to the QED Vacuum Energy

At energies much less than the electron mass $m$ the effects of quantum fluctuations in the vacuum due to virtual electron loops can be included by extending the Maxwell Lagrangian by additional non-renormalizable terms corresponding to the Uehling and Euler-Heisenberg interactions. This effective field theory is used to calculate the properties of the QED vacuum at temperatures $T << m$. By a redefinition of the electromagnetic field, the Uehling term is shown not to contribute. The Stefan-Boltzmann energy density is thus found to be modified by a term proportional with $T^8/m^4$ in agreement with the semi-classical result of Barton. The speed of light in blackbody radiation is smaller than one. Similarly, the correction to the energy density of the vacuum between two metallic parallel plates diverges like $1/m^4z^8$ at a distance from one of the plates $z \to 0$. While the integral of the regularized energy density is thus divergent, the regularized integral is finite and corresponds to a correction to the Casimir force which varies with the separation $L$ between the plates as $1/m^4L^8$. This result is in seemingly disagreement with a previous result for the radiative correction to the Casimir force which gives a correction varying like $1/mL^5$ in a calculation using full QED.

hep-ph↗
arXiv1997

Radiative Corrections to the Stefan-Boltzmann Law

Photons in blackbody radiation have non-zero interactions due to their couplings to virtual electron-positron pairs in the vacuum. For temperatures much less than the electron mass $m$ these effects can be described by an effective theory incorporating the Uehling and Euler-Heisenberg interactions as dominant terms. By a redefinition of the electromagnetic field, the Uehling term is shown not to contribute. The Stefan-Boltzmann energy is then modified by a term proportional with $T^8/m^4$ in agreement with the semi-classical result of Barton. The same effects give a speed of light smaller than one at non-zero temperatures as has also recently been derived using full QED.

hep-ph↗
arXiv1997

Applications of Effective Lagrangians

Effective Lagrangians were originally used only at the tree level as so-called phenomenological Lagrangians since they were in general non-renormalizable. Today they are treated as effective field theories valid below a characteristic energy scale. Quantum corrections can then be calculated in a consistent way as for any renormalizable theory. A few applications of the Euler-Heisenberg Lagrangian for interacting photons at low energies are presented together with recent developments in the use of QED for non-relativistic systems. Finally, the ingredients of an effective theory for the electroweak sector of the Standard Model are discussed in the case of a non-linear realization of the Higgs mechanism using the Stuckelberg formalism. [Invited talk at "Beyond the Standard Model V", Balholm, Norway, April 29 - May 4, 1997]

hep-ph↗
arXiv1997

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.

quant-ph↗
arXiv1997

What is the Regularized Casimir Vacuum Energy Density?

The regularized total Casimir energy in spacetimes with boundaries is not in general equal to the integral of the regularized energy density. This paradoxical phenomenon is most transparently analyzed in the simple example of a massless scalar field in 1+1 dimensions confined to a line element of length $L$ and obeying Dirichlet boundary conditions.

quant-ph↗