Interpretation of Quantum Field Theories with a Minimal Length Scale

It has been proposed that the incorporation of an observer independent minimal length scale into the quantum field theories of the standard model effectively describes phenomenological aspects of quantum gravity. The aim of this paper is to interpret this description and its implications for scattering processes.Comment: replaced with published versio

Higgs Boson in RG running Inflationary Cosmology

An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for finely tuned values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.Comment: 7 pages, no figur

Unified theory for external and internal attributes and symmetries of fundamental fermions

An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the triple-direct-products of Dirac gamma-matrices and a triple-spinor-field, called a triplet field, defined on the algebra. The algebra possesses three commutative sub-algebras which describe, respectively, the external space-time symmetry, the family structure and the internal color symmetry of quarks and leptons. The triplet field includes threefold (fourfold) repetitionary modes of spin 1/2 component fields with SU(3) (SU(4)) color symmetry. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The Dirac mass matrices with quasi-democratic structure are derived as an illustration

Theory of Complex Scattering Lengths

We derive a generalized Low equation for the T-matrix appropriate for complex atom-molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.Comment: 9 page

The Solar Proton Burning Process Revisited In Chiral Perturbation Theory

The proton burning process p + p -> d + e(+) + \nu(e), important for the stellar evolution of main-sequence stars of mass equal to or less than that of the Sun, is computed in effective field theory using chiral perturbation expansion to the next-to-next-to leading chiral order. This represents a model-independent calculation consistent with low-energy effective theory of QCD comparable in accuracy to the radiative np capture at thermal energy previously calculated by first using very accurate two-nucleon wavefunctions backed up by an effective field theory technique with a finite cut-off. The result obtained thereby is found to support within theoretical uncertainties the previous calculation of the same process by Bahcall and his co-workers.Comment: 30 pages, 2 eps files, aaspp4.sty needed, slightly modified, to be published in Ap.

The resultant parameters of effective theory

This is the 4-th paper in the series devoted to a systematic study of the problem of mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of essential parameters in the case of the most general effective scattering theory containing no massless particles with spin J > 1/2. We perform the detailed classification of combinations of the Hamiltonian coupling constants and select those which appear in the expressions for renormalized S-matrix elements at a given loop order.Comment: 21 pages, 4 LaTeX figures, submitted to Phys. Rev.

Six-dimensional Methods for Four-dimensional Conformal Field Theories

The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields on the hypercone in six-dimensional projective space, satisfying certain transversality conditions. In this way some Green's functions in conformal field theories are shown to have structures more general than those commonly found by use of the inversion operator. These methods fit in well with the assumption of AdS/CFT duality. In particular, it is transparent that if fields on AdS$_5$ approach finite limits on the boundary of AdS$_5$, then in the conformal field theory on this boundary these limits transform with conformal dimensionality zero if they are tensors (of any rank), but with conformal dimension 1/2 if they are spinors or spinor-tensors.Comment: Version accepted for publication in Physical Review D. References to earlier work added in footnote 2. Minor errors corrected. 24 page

Spontaneous violation of CP symmetry in the strong interactions

Some time ago Dashen pointed out that spontaneous CP violation can occur in the strong interactions. I show how a simple effective Lagrangian exposes the remarkably large domain of quark mass parameters for which this occurs. I close with some warnings for lattice simulations.Comment: 10 pages, 1 figure; final version to appear in PR

II. The Standard Model in the Isotopic Foldy-Wouthuysen Representation without Higgs Bosons in the Fermion Sector. Spontaneous Breaking of Parity and "Dark Matter" Problems

The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(2)xU(1) - invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently, it is not necessary to introduce interactions between Higgs bosons and fermions. The study discusses a possible relation between spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles of "dark matter".Comment: 12 page