Magnetic field induced rotation of the d-vector in Sr_2RuO_4

The superconductor Sr_2RuO_4 is widely believed to be a spin triplet system with a chiral order parameter analogous to the A phase of superfluid helium-3. The best evidence for this pairing state is that the Knight shift or spin susceptibility measured in neutron scattering is constant below T_c, unlike in a spin-singlet superconductor. The original Knight shift and neutron scattering measurements were performed for magnetic fields aligned in the ruthenate a-b plane. These would be consistent with a triplet d-vector d{k} aligned along the c-axis. However recently the Knight shift for fields along c was also found to be constant below T_c, which is not expected for this symmetry state. In this paper we show that while spin-orbit interaction stabilises the c-axis oriented d-vector, it is possible that only a very small external B field may be sufficient to rotate the d-vector into the a-b plane. In this case the triplet pairing model remains valid. We discuss characteristics of the transition and the prospects to detect it in thermodynamic quantities.Comment: 2 pages, 1 figure, Proceedings of the M2S-HTSC conference in Dresden. Requires elsart.sty (included

Renormalization Group and Decoupling in Curved Space: II. The Standard Model and Beyond

We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The QCD sector at low-energies is described in terms of the composite effective fields. For fermions and scalars the massless limit shows perfect correspondence with the conformal anomaly, but similar limit in a massive vector case requires an extra compensating scalar. In all three cases the decoupling goes smoothly and monotonic. A particularly interesting case is the renormalization group flow in the theory with broken supersymmetry, where the sign of one of the beta-functions changes on the way from the UV to IR.Comment: 27 pages, 8 figure

Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime

The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the $\lambda \varphi^4$-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the $\lambda \varphi^4$-theory on a De Sitter background.Comment: 18 pages, LaTeX file, UB-ECM-PF 93/2

The Lantern Vol. 14, No. 1, December 1945

• Editorial • The Medal • Pain • Wonder • Warmth • Memory Lingers • Morning • Watch the Birdie • Poems • The War Dogs of the Devildogs • Joy in Every Heart • To Live in Hearts • The Operation • Moderately Well Done • Steak is King • Grateful America?https://digitalcommons.ursinus.edu/lantern/1037/thumbnail.jp

The Lantern Vol. 14, No. 1, December 1945

• Editorial • The Medal • Pain • Wonder • Warmth • Memory Lingers • Morning • Watch the Birdie • Poems • The War Dogs of the Devildogs • Joy in Every Heart • To Live in Hearts • The Operation • Moderately Well Done • Steak is King • Grateful America?https://digitalcommons.ursinus.edu/lantern/1037/thumbnail.jp

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

Contact Interactions Involving Right-handed Neutrinos and SN1987A

We consider lepton-quark contact interactions in models with right-handed neutrinos, and find that observational data from SN1987A restricts the scale of such interactions to be at least $\Lambda>90$ TeV.Comment: 7 pages, latex, no figures. Minor corrections to match final version to appear in Phys. Rev.

Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint