arXiv subjects

Peter E. Haagensen

Publications and source records attributed to Peter E. Haagensen.

13 recordsLinked to original sources

arXiv1998

Finite Quantum Fluctuations About Static Field Configurations

We develop an unambiguous and practical method to calculate one-loop quantum corrections to the energies of classical time-independent field configurations in renormalizable field theories. We show that the standard perturbative renormalization procedure suffices here as well. We apply our method to a simplified model where a charged scalar couples to a neutral "Higgs" field, and compare our results to the derivative expansion.

hep-th↗

arXiv1997

Two-Loop Beta Functions Without Feynman Diagrams

Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained without Feynman diagram calculations, and represents further evidence that duality symmetry severely constrains renormalization flows.

hep-th↗

arXiv1997

Duality and the Renormalization Group

The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field theoretical systems. After a review of what has been accomplished in the context of 2d sigma models, new results are presented which set up the stage for a fully generic calculation at two-loop order, with particular emphasis on the question of scheme dependence.

hep-th↗

arXiv1997

T-Duality and Two-Loop Renormalization Flows

Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the target. For a restricted background, T-duality transformations are then studied at the next order, and the ensuing consistency conditions are found to be satisfied by the two-loop Weyl anomaly coefficients of the model. This represents an extremely non-trivial test of the covariance of renormalization group flows under T-duality, and a stronger condition than T-duality invariance of the string background effective action.

hep-th↗

arXiv1997

On the Wavefunctional for Two Heavy Color Sources in Yang-Mills Theory

In an abelian gauge theory, the Coulombic potential between two static charges is obtained most directly when a correct separation between gauge-invariant and gauge degrees of freedom is made. This motivates a similar separation in the nonabelian theory. When a careful identification of the Hilbert space is made, along with the proper analyticity requirements, it is then possible to find the appropriate wavefunctionals describing heavy color sources in the theory. This treatment is consistent with, and realizes in a simple way the center symmetry Z_N of SU(N) gauge theories.

hep-th↗

arXiv1996

Duality Transformations Away From Conformal Points

Target space duality transformations are considered for bosonic sigma models and strings away from RG fixed points. A set of consistency conditions are derived, and are seen to be nontrivially satisfied at one-loop order for arbitrary running metric, antisymmetric tensor and dilaton backgrounds. Such conditions are sufficiently stringent to enable an independent determination of the sigma model beta functions at this order.

hep-th↗

arXiv1995

Gauge Invariant Geometric Variables For Yang-Mills Theory

In a previous publication [1], local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.

hep-th↗

arXiv1995

New Gauge Invariant Variables for Yang-Mills Theory

A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance found to hold for the basic equations and commutators of the theory in the canonical formalism. We emphasize, however, that we are not interested in and do not consider the coupling of the theory to gravity. We concentrate here on a technical difficulty of this approach, the calculation of the electric field energy. This in turn hinges on the well-definedness of the transformation of variables, an issue which is settled through degenerate perturbation theory arguments.

hep-th↗

arXiv1995

Yang-Mills Fields and Riemannian Geometry

It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gauss' law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover further constraints physical states must satisfy. For gauge group $SU(2)$, the underlying geometry is Riemannian and based on the group $GL(3)$. The formalism allows also for the inclusion of static color sources and the extension to gauge groups $SU(N>2)$, both of which are discussed here.

hep-th↗

arXiv1994

The Exact Renormalization Group and Approximations

We review the Exact Renormalization Group equations of Wegner and Houghton in an approximation which permits both numerical and analytical studies of nonperturbative renormalization flows. We obtain critical exponents numerically and with the local polynomial approximation (LPA), and discuss the advantages and shortcomings of these methods, and compare our results with the literature. In particular, convergence of the LPA is discussed in some detail. We finally integrate the flows numerically and find a $c$-function which determines these flows to be gradient in this approximation.

hep-th↗

arXiv1993

Gradient Flows from an Approximation to the Exact Renormalization Group

Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions $d_k={2k\over k-1}$, $k=2,3,4,\ldots$ appear naturally encoded in our formalism, and for dimensions smaller but very close to $d_k$ our results match the $\ee$-expansion. Within the coupling constant subspace of mass and quartic couplings and for any $d$, we find a gradient flow with two fixed points determined by a positive-definite metric and a $c$-function which is monotonically decreasing along the flow.

hep-th↗

arXiv1992

A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order

We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all 1- and 2-loop 1PI diagrams, run renormalization group equations on them and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle $γ_5$ problems.

hep-ph↗

arXiv1991

Differential Renormalization of the Wess-Zumino Model

We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $β$-function is computed to three loops and is found to agree with previous existing results. As a further, nontrivial check of the method, the Callan-Symanzik equations are also verified to that loop order. Finally, we argue that differential renormalization presents advantages over other superspace renormalization methods, in that it avoids both the ambiguities inherent to supersymmetric regularization by dimensional reduction (SRDR), and the complications of virtually all other supersymmetric regulators.

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