Calculation Of Quantum Effects Research Articles

Renormalization group for nonminimal ϕ2R couplings and gravitational contact interactions

Theories of scalars and gravity, with an Einstein-Hilbert term and nonminimal interactions, ${M}^{2}R/2\ensuremath{-}\ensuremath{\alpha}{\ensuremath{\phi}}^{2}R/12$, have graviton exchange-induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $\ensuremath{\alpha}$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $\ensuremath{\alpha}$ is absent, for small steps in scale $\ensuremath{\delta}\ensuremath{\mu}/\ensuremath{\mu}$ infinitesimal contact terms $\ensuremath{\sim}\ensuremath{\delta}\ensuremath{\alpha}$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $\ensuremath{\beta}$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.

Technically natural cosmological constant from supersymmetric 6D brane backreaction

Abstract We provide an explicit example of a higher-dimensional model describing a non-supersymmetric spectrum of 4D particles of mass M, whose 4D geometry – including loop effects – has a curvature that is of order R ∼ m K K 4 / M p 2 , where m K K is the extra-dimensional Kaluza–Klein scale and Mp is the 4D Planck constant. m K K is stabilized and can in particular satisfy m K K ≪ M . The system consists of a (5+1)-dimensional model with a flux-stabilized supersymmetric bulk coupled to non-supersymmetric matter localized on a (3+1)-dimensional positive-tension brane. We use recent techniques for calculating how extra dimensions respond to changes in brane properties to show (at the classical level) that the extra-dimensional volume adjusts to ensure that the low-energy 4D geometry is exactly flat, independent of the value of the brane tensions. Its mechanism for doing so is the transfer of stabilizing flux between the bulk and the branes. The UV completion of the model can arise at scales much larger than M, allowing the calculation of quantum effects like the zero-point energy of very massive particles in the vacuum. We find that brane-localized loops do not affect the 4D curvature at all, but bulk loops can. These can be estimated on general grounds and we show that supersymmetry dictates that they generate curvatures that are generically of order m K K 4 / M p 2 . For realistic applications this points to a world with two supersymmetric extra dimensions, with supersymmetry in the bulk broken at the sub-eV KK scale – as proposed in hep-th/0304256 – requiring a 6D gravity scale somewhat higher than 10 TeV. Ordinary Standard Model particles are brane-localized and not at all supersymmetric (implying in particular no superpartners or the MSSM). We discuss how the model evades various no-go theorems that would naively exclude it, and briefly outline several striking observational implications for tests of gravity and at the LHC.

Axially symmetric multi-instanton solutions generated by conformal mappings

It is shown that exact axially symmetric, regular self-dual multi-instanton solutions of the SU(2) Yang-Mills equations can be generated from the vacuum solution by means of singular conformal mappings of a complex plane followed by a singular gauge transformation. The regularizing gauge for the 't Hooft singular solution is found and the corresponding Yang-Mills gauge potential ${\mathit{A}}_{\ensuremath{\mu}}$ without any singularity and with the correct asymptotic behavior is given. The relations between the parameters in different forms of the solution are explored and the possible implications on the calculations of quantum effects are noted.

Equilibrium properties of fluids in the semiclassical limit. II. Application to hard-sphere fluids

We present computationally convenient theoretical methods for calculating the structural and thermodynamic properties of a fluid in the semiclassical limit where quantum effects are small. The concept of the effective two-body Mayer functions has been used to develop two approximations, one for the pair correlation function and the other for the Helmholtz free energy. The theory has been applied to the calculation of quantum effects on the radial distribution function and Helmholtz free energy of a fluid of hard spheres. It is shown that because of quantum effects a significant change in the structure of a hard-sphere fluid takes place in the neighborhood of the point of contact.