Instantons and vacuum expectation values in the Schwinger model

Vacuum expectation values for the Schwinger model are computed within the path integral formalism for an instanton vacuum. The calculations are done in flat Euclidean space and use the wellknown anomaly result. It can be demonstrated that the instanton vacuum is absolutely necessary to obtain a consistent quantization. At last the results are compared to a similar treatment on the sphere and to the operator solution of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. P8444-TEC     

Aspects of the functional renormalisation group

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.     

Calculating infrared contributions to vacuum expectation values of gluonic and quark fields

Based on the infrared asymptotics of the lower QCD Green's functions obtained before, we propose a definition and elaborate a technique for calculating non-perturbative vacuum expectations of gluon and quark fields. In our calculations, we use only the known QCD parameters: constitutent quark masses, the confining potential slope and the QCD parameter Γ. The values obtained for the vacuum expectations agree well with experiment.     

Higgs boson production at CLIC in SUSY models with hierarchy of the vacuum expectation values

Many theoretical schemes predict the existence of unconventional quarks and leptons not fitting the standard pattern of fermion families. We consider two possible kinds of non-standard fermions, mirror fermions and exceptional fermions. Mirror fermions arise in a variety of models ranging from family unification to extended supersymmetry and Kaluza-Klein theories; exceptional fermions come along with the groupE ₆ which is believed to be the low energy gauge symmetry of the superstring theory. We discuss some physical properties of these non-standard particles relevant for the LEP     

Series expansion solution of the Wegner-Houghton renormalisation group equation

The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for then-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors.     

Unconventional model of neutrino masses

Gelmini and Roncadelli have proposed a model of neutrino masses in which B?L symmetry is spontaneously broken by a small vacuum expectation value of a Higgs triplet. We give an exegesis of this model. We show that the massive neutrinos in this model cannot be cosmologically relevant today and that conflicting analyses of double beta decay experiments can be reconciled.     

Prospects for superstring models with two vacuum expectation values for standard model singlets

The spontaneous breaking of rank-six intermediate groups to the standard model in superstring phenomenology is examined. It requires the existence of two vacuum expectation values, one for each standard model singlet in the 27 chiral representation of E₆. We use a simplified model based on the group SU(3)_c×SU(2)_L×SU(2)_R×U(1)_L×U(1)_R. It is found that the well-known phenomenological constraints such as proton decay, vanishing neutrino masses and flavour-changing neutral currents allow for the possibility of sizeable Yukawa couplings for the two standard model singlets which can originate low energy negative masses. The proof of this radiative breaking relies, however, on several parameters whose magnitude is unpredicted, but is facilitated if the mass of the exotic quark is large (∼300 GeV).     

Majorana neutrino masses in the three-flavor Pauli model

A special Majorana model for three neutrino flavors is developed on the basis of the Pauli transformation group. In this model, the neutrinos possess a partially conserved generalized lepton (Pauli) charge that makes it possible to discriminate between neutrinos of different type. It is shown that, within the model in question, a transition from the basic “mass” representation, where the average value of this charge is zero, to the representation associated with physical neutrinos characterized by specific Pauli “flavor” charges establishes a relation between the neutrino mixing angles θ _{mix, 12}, θ _{mix, 23}, and θ _{mix, 13} and an additional relation between the Majorana neutrino masses. The Lagrangian mass part, which includes a term invariant under Pauli transformations and a representation-dependent term, concurrently assumes a “quasi-Dirac” form. With allowance for these relations, the existing set of experimental data on the features of neutrino oscillations makes it possible to obtain quantitative estimates for the absolute values of the neutrino masses and the 2β-decay mass parameter m _ββ and a number of additional constraints on the neutrino mixing angles.     

Gradient properties of the renormalisation group equations in multicomponent systems

The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ⁴ interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed.     

Models of neutrino masses and mixings

I discuss models of neutrino masses that could lead to a large mixing angle for the atmospheric neutrino oscillations.     

Theory of neutrino masses and mixing

We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and discuss their applications. We exemplify these theoretical concepts with the groups S ₄ and A ₄. Finally, we discuss the relation between tensor products of irreducible representations and Yukawa couplings and describe a model for tri-bimaximal lepton mixing based on A ₄.     

Models of neutrino masses and baryogenesis

Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to discriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet Higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.     

Quantum dissipation in vacuum neutrino oscillation

The pattern of neutrino oscillations changes when one considers these particles evolving as an open quantum system. In this article we derive seven possibilities that change the two-generation neutrino survival probability due to quantum dissipation and decoherence. We find entirely original probabilities assuming that these effects can be parametrized by the addition of only one phenomenological constant keeping complete positivity. We observe that a relaxation effect of the system shows an unusual mechanism of flavor conversion, the appearance of CP-violation effects for Majorana neutrinos, besides an appreciable change in the behavior of high energy neutrinos.     

On the characterization of relativistic quantum field theories in terms of finitely many vacuum expectation values. II

The problem of uniqueness of monotone continuous linear extensions of $$T_{(2N)} = \{ 1,T_1 ,...,T_{2N} \} \in E'_{(2N)} = \prod\limits_{n = 0}^{2N} {E'_n } $$ is solved. A characterization of a relativistic QFT in terms of finitely many VEV's is derived. All results are illustrated by an explicit discussion of the extension problem for special cases ofT ₍₄₎={1,0,T ₂,T ₃,T ₄}. This discussion contains explicitly necessary and sufficient conditions onT ₍₄₎ for the existence of minimal extensions and some convenient sufficient conditions.