New results for two-loop off-shell three-point diagrams

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.Comment: 10 pages, 3 figures, standard LaTEX (PS-file is also available by anonymous FTP at node VSFYS1.FI.UIB.NO in subdirectory DAVYDYCHEV, the file BERGEN94-03.PS), Bergen Scientific/Technical Report No.1994-0

Validation of the Dutch Freiburg mindfulness inventory in patients with medical illness

Most validation studies of the Freiburg Mindfulness Inventory (FMI) involved healthy subjects. Validation in patients who suffer from a life-threatening medical illness is needed, to investigate the FMI’s validity in medical psychology research and practice. Psychometric properties of the Dutch FMI were examined in two patient groups of two different studies: (Sample 1) cardiac patients (n = 114, M age = 56 ± 7 years, 18% women) and (Sample 2) severely fatigued cancer survivors (n = 158, M age = 50 ± 10 years, 77% women). Confirmatory factor analysis (studied only in Sample 2) provided good fit for the two-factor solution (Acceptance and Presence), while the one-factor solution provided suboptimal fit indices. Internal consistency was good for the whole scale in both samples (Sample 1 α = .827 and Sample 2 α = .851). The two-factor model showed acceptable to good internal consistency in Sample 2 (Presence: α = .823; Acceptance α = .744), but poor to acceptable in Sample 1 (Presence subscale: α = .577, Acceptance subscale: α = .791). Clinical sensitivity was supported in both samples, and construct validity (studied only in Sample 1) was acceptable. The Dutch FMI is an acceptable instrument to measure mindfulness in patients who experienced a life-threatening illness in a Dutch-speaking populatio

Infinities within graviton scattering amplitudes

We present unitarity as a method for determining the infinities present in graviton scattering amplitudes. The infinities are a combination of IR and UV. By understanding the soft singularities we may extract the UV infinities and relate these to counter-terms in the effective action. As an demonstration of this method we rederive the UV infinities present at one-loop when gravity is coupled to matter.Comment: revised versio

Dimensional Reduction in Non-Supersymmetric Theories

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.Comment: 13 pages, phyzzx, LTH 32

Symmetry breaking from Scherk-Schwarz compactification

We analyze the classical stable configurations of an extra-dimensional gauge theory, in which the extra dimensions are compactified on a torus. Depending on the particular choice of gauge group and the number of extra dimensions, the classical vacua compatible with four-dimensional Poincar\'e invariance and zero instanton number may have zero energy. For SU(N) on a two-dimensional torus, we find and catalogue all possible degenerate zero-energy stable configurations in terms of continuous or discrete parameters, for the case of trivial or non-trivial 't Hooft non-abelian flux, respectively. We then describe the residual symmetries of each vacua.Comment: 24 pages, 1 figure, Section 4 modifie

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space ${\cal F}^{+}({\sf H}_{\rm graviton})$ where the one-particle Hilbert space ${\sf H}_{graviton}$ carries the direct sum of two unitary irreducible representations of the Poincar\'e group corresponding to two particles of mass $m > 0$ and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type $Ker(Q)/Im(Q)$ where $Q$ is a gauge charge defined in an extension of the Hilbert space ${\cal H}_{\rm graviton}$ generated by the gravitational field $h_{\mu\nu}$ and some ghosts fields $u_{\mu}, \tilde{u}_{\mu}$ (which are vector Fermi fields) and $v_{\mu}$ (which are vector field Bose fields.) Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.Comment: 35 pages, no figur

Confinement, Chiral Symmetry Breaking, and Axial Anomaly from Domain Formation at Intermediate Resolution

Based on general renormalization group arguments, Polyakov's loop-space formalism, and recent analytical lattice arguments, suggesting, after Abelian gauge fixing, a description of pure gluodynamics by means of a Georgi-Glashow like model, the corresponding vacuum fields are defined in a non-local way. Using lattice information on the gauge invariant field strength correlator in full QCD, the resolution scale \La_b, at which these fields become relevant in the vacuum, is determined. For SU(3) gauge theory it is found that \La_b\sim 2.4 GeV, 3.1 GeV, and 4.2 GeV for ($N_F=4, m_q=18$ MeV), ($N_F=4, m_q=36$ MeV), and pure gluodynamics, repectively. Implications for the operator product expansion of physical correlators are discussed. It is argued that the emergence of magnetic (anti)monopoles in the vacuum at resolution \La_b is a direct consequence of the randomness in the formation of a low entropy Higgs condensate. This implies a breaking of chiral symmetry and a proliferation of the axial U(1) anomaly at this scale already. Justifying Abelian projection, a decoupling of non-Abelian gauge field fluctuations from the dynamics occurs. The condensation of (anti)monopoles at \La_c<\La_b follows from the demand that vacuum fields ought to have vanishing action at any resolution. As monopoles condense they are reduced to their cores, and hence they become massless. Apparently broken gauge symmetries at resolutions \La_c<\La\le\La_b are restored in this process.Comment: 11 pages, 3 figure

Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory

We discuss the renormalization of a BRST and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with the general BRST and anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this study stems from a recent claim that the non-vanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with the previous works and argue the physical implications of the obtained results.Comment: 49 pages, 35 eps-files, A number of typographic errors are corrected. A paragraph is added in the beginning of section 5.3. Two equations (7.1) and (7.2) are added. A version to be published in Phys. Rev.

Two-loop three-gluon vertex in zero-momentum limit

The two-loop three-gluon vertex is calculated in an arbitrary covariant gauge, in the limit when one of the external momenta vanishes. The differential Ward-Slavnov-Taylor (WST) identity related to this limit is discussed, and the relevant results for the ghost-gluon vertex and two-point functions are obtained. Together with the differential WST identity, they provide another independent way for calculating the three-gluon vertex. The renormalization of the results obtained is also presented.Comment: 22 pages, LaTeX, including 4 figures, uses eps

Confinement in Covariant Gauges

We examine the weak coupling limit of Euclidean SU(n) gauge theory in covariant gauges. Following an earlier suggestion, an equivariant BRST-construction is used to define the continuum theory on a finite torus. The equivariant gauge fixing introduces constant ghost fields as moduli of the model. We study the parameter- and moduli- space perturbatively. For $n_f \leq n$ quark flavors, the moduli flow to a non-trivial fixed point in certain critical covariant gauges and the one-loop effective potential indicates that the global SU(n) color symmetry of the gauge fixed model is spontaneously broken to $U(1)^{n-1}$. Ward identities and renormalization group arguments imply that the longitudinal gauge boson propagator at long range is dominated by $n(n-1)$ Goldstone bosons in these critical covariant gauges. In the large $n$ limit, we derive a nonlinear integral equation for the expectation value of large Wilson loops assuming that the exchange of Goldstone bosons dominates the interaction at long range in critical covariant gauges. We find numerically that the expectation value of large circular Wilson loops decreases exponentially with the enclosed area in the absence of dynamical fermions. The gauge invariance of this mechanism for confinement in critical covariant gauges is discussed.Comment: 45 pages, Latex, uses psfig.sty and epsfig.sty to include postscript-figure