Foundational aspects of geometro-stochastic quantization of Dirac fields in curved spacetime

The application of the recently developed method of geometro-stochastic quantization to spin-1/2 fields in curved spacetime does not give rise to any of the conceptual and technical difficulties encountered by more conventional methods of quantization. Field propagation is based on the concept of stochastic parallel transport governed by quantum connections that incorporate Poincaré gauge invariance and obey the equivalence principle. Consequently, under free-fall conditions, such geometro-stochastic Dirac field propagation does not give rise to Bogolubov transformations resulting in spontaneous fermion creation.1. Supported in part by the NSERC Research Grant No. A5206.2. Supported by an NSERC postgraduate fellowship.     

Cosmic strings in a space–time with positive cosmological constant

We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

Kaluza–Klein modes of bulk fields in a generalized Randall–Sundrum scenario

We consider a generalised two brane Randall–Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza–Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb–Ramond field in a such generalized Randall–Sundrum scenario are determined. The masses for the Kaluza–Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology.     

Quantization of fermions interacting with point-like external fields

A second quantization of a four-parameter family of Dirac operators interacting with point-like fields leads to inequivalent representations of the CAR. Implementability of gauge transformations gives quantization conditions. We determine the algebra of charges, identify the Schwinger term, and work out a connection between the Fredholm index and the winding number.Supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P5588.     

Self duality of the gauge field equations and the cosmological constant

This paper considers the Einstein equations coupled with the nonabelian gauge and Higgs fields. It is shown that, when cosmic string solutions are sought in the Einstein-Georgi-Glashow system and the Einstein-Weinberg-Salam system governing the gravitational-electromagnetic-weak interaction forces, the self duality conditions lead to positive values of the cosmological constant which can be expressed by some fundamental parameters in particle physics.     

A unified gauge and gravity theory with only matter fields

We propose a purely fermionic action with gauge and general relativistic invariances. This implies a unified treatment of gravity and gauge theories without elementary metric tensor and gauge boson fields. At the quantum level this scale-invariant theory generates, as vacuum properties, both a metric and a scale Λ which becomes related to the Planck mass. The analysis of the spectrum displays, besides the original fermions, massless composite vierbein and gauge bosons, as well as a set of states with masses of order Λ. In a low-energy regime in which these heavy modes are not excited, the light sector is shown to be governed by a phenomenological action which coincides with the conventional gravity-gauge-matter theory without cosmological term and with a Newton constant and gauge couplings determined by Λ. For increasing energies, the gauge interactions are predicted to grow towards their merging with gra Λ, the theory differs substantially from the conventional one, not even allowing a definition of a space-time metric and providing hints for a milder ultraviolet behaviour.     

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained. Supported by Knowledge Innovation Project of the Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N02 and KJCX2-SW-N016), the National Natural Science Foundation of China (Grant Nos. 10435080 and 10575123), Beijing Natural Science Foundation (Grant No. 1072005) and the Science and Technology Development Foundation of Beijing Municipal Education Committee (Grant No. Km200310005018)     

Parent Field Theory and Unfolding in BRST First-Quantized Terms

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.Senior Research Associate of the National Fund for Scientific Research (Belgium).Postdoctoral Visitor of the National Fund for Scientific Research (Belgium).     

一种自对偶理论的规范不变形式及其量子化

对于一种新提出的自对偶场与规范场耦合的拉氏理论,本文给出相应的单上闭链,即Wess-Zumino项,构造了这种理论的规范不变的形式。利用正则量子化方法并通过选取适当的规范固定条件,证明了这规范不变的形式等价于原来的规范非不变的形式。此外,利用Batalin-Fradkin-Vilkovisky量子化方法,进一步指出这种等价性与规范固定条件的选择是无关的。 关键词：     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Absolute minima of the higgs potential with vanishing cosmological constant in N=1 supergravity GUTs

A necessary condition is derived for the desired vacuum to be an absolute minimum of the scalar potential with vanishing cosmological constant. In the case of a renormalizable GUT-sector this implies the existence of physical light chiral superfields which transform like the Goldstone fields associated with the braking of the GUT-symmetry. Via the renormalization of gauge couplings these lead to a small unification scale and thus to disastrous proton decay rates.     

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.     

Relation between nonlinear models and gauge ambiguities

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear -models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group).Supported in part by the U.S. Department of Energy.Supported by Fonds zur Förderung der Wissenschaftlichen Forschung in Österreich     

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

In this paper, we investigate the generalized Saez–Ballester scalar–tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.     

Geometro-stochastic quantization of gravity. I

A general method of geometro-stochastic first quantization is outlined, and then applied to the construction of a graviton bundleE. This quantization is performed by treating the graviton as a massless stringlike exciton of spin 2, whose states can be represented by the vectors in the bundleE over a base manifoldM of mean spacetime locations. The graviton bundleE carries an indefinite inner product, and possesses both external Poincaré gauge degrees of freedom, as well as internal gauge degrees of freedom related to general changes of coordinates in an immediate neighbourhood of eachx M. 1. Supported in part by the NSERC Research Grant No. A5206.     

Renormalization of an abelian gauge theory in stochastic quantization

The renormalization of an abelian gauge field coupled to a complex scalar field is disccused in the stochastic quantization method. The supper space formulation of the stochastic quantization method is used to derived the Ward Takahashi identities assocoated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahshi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constant in temrs of scaling of the fields and of the parameters appearing in the stochastic theory.