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Hidenori Sonoda

Publications and source records attributed to Hidenori Sonoda.

54 records · Page 3Linked to original sources
arXiv2001

Off-shell renormalization of the massive QED in the unitary gauge

Despite its simplicity, the unitary gauge is not a popular choice for practical loop calculations in gauge theories, due to the lack of off-shell renormalizability. We study the renormalization properties of the off-shell Green functions of the elementary electron fields in the massive QED, in order to elucidate the origin and structure of the extra ultraviolet divergences which exist only in the unitary gauge. We find that all these divergences affect the Green functions in a trivial way such that in coordinate space the off-shell Green functions are in fact multiplicatively renormalizable. This result may generalize to the abelian and non-abelian Higgs theories, for which the unitary gauge might bring much simplification to the loop calculations.

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arXiv2000

On the gauge parameter dependence of QED

The gauge parameter dependence of QED in the covariant gauge can be determined explicitly by introducing a Stueckelberg field, which is a non-interacting fictitious Goldstone boson field. Examples of QED with electrons or charged scalars are discussed. Our results generalize the long known results on the gauge parameter dependence of the wave function renormalization constant and the electron propagator.

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arXiv2000

Chiral QED out of matter

In a previous paper we have shown how the Wilsonian renormalization group naturally leads to the equivalence of the standard QED with a matter-only theory. In this paper we give an improved explanation of the equivalence and discuss, as an example, the equivalence of a chiral QED in the Higgs phase with a matter-only theory. Ignoring the contributions suppressed by the negative powers of a UV cutoff, the matter-only theory is equivalent to the perturbatively renormalizable chiral QED with two complex Higgs fields. In the matter-only theory chiral anomaly arises without elementary gauge fields.

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arXiv2000

QED out of matter

The Wilsonian renormalization group implies that an arbitrary four dimensional field theory with an ultraviolet cutoff is equivalent to a theory which is renormalizable by power counting at energy scales much below the cutoff. This applies to any theory including those with non-renormalizable interactions as long as we fine-tune the mass parameters. We analyze two simple models with current-current interactions but without elementary gauge fields from this viewpoint. We show how to tune the parameters of the models so that they become equivalent to QED at energies much below the cutoff.

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arXiv1999

Bose condensation at high temperatures

Bose condensation is usually a low temperature phenomenon due to a low particle number density. When the number density is kept large compared to the inverse Compton volume, Bose condensation can occur at a temperature much higher than the mass of the particle. We can then use a three dimensional effective theory to study the thermal properties. We compute the transition temperature for a complex scalar field theory with a small interaction parameter.

hep-ph↗
arXiv1998

Phase transition of a scalar field theory at high temperatures

At high temperatures a four dimensional field theory is reduced to a three dimensional field theory. In this letter we consider the $ϕ^4$ theory whose parameters are chosen so that a thermal phase transition occurs at a high temperature. Using the known properties of the three dimensional theory, we derive a non-trivial correction to the critical temperature.

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arXiv1996

Understanding Chiral Anomaly in Coordinate Space

By completing the old discussion of K.~Wilson, we express the chiral anomaly in terms of a double integral of a three-point function of chiral currents over an arbitrarily small region in the coordinate space. An integrability condition provides an important finite local counterterm to the integral.

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arXiv1995

The Energy-Momentum Tensor in Field Theory II

In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the energy-momentum tensor over space, where the short distance singularities of the product of the energy-momentum tensor and an arbitrary composite field must be subtracted, and finite counterterms must be added. These finite counterterms have been interpreted geometrically as a connection for the linear space of composite fields over theory space. In this paper we will study a second order consistency condition for the variational formula and determine the torsion of the connection. A non-vanishing torsion results from the integrability of the variational formula, and it is related to the Bose symmetry of the product of two energy-momentum tensors. The massive Ising model on a curved two-dimensional surface is discussed as an example, and the short-distance singularities of the product of two energy-momentum tensors are calculated explicitly.

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arXiv1995

The Energy-Momentum Tensor in Field Theory I

This is the first of three papers on the short-distance properties of the energy-momentum tensor in field theory. We study the energy-momentum tensor for renormalized field theory in curved space. We postulate an exact Ward identity of the energy-momentum tensor. By studying the consistency of the Ward identity with the renormalization group and diffeomorphisms, we determine the short-distance singularities in the product of the energy-momentum tensor and an arbitrary composite field in terms of a connection for the space of composite fields over theory space. We discuss examples from the four-dimensional $ϕ^4$ theory. In the forthcoming two papers we plan to discuss the torsion and curvature of the connection.

hep-th↗
arXiv1994

A Scheme Independent Definition of $Λ_{\rm QCD}$

Given a renormalization scheme of QCD, one can define a mass scale $Λ_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $Λ_{\rm QCD}$ changes by a multiplicative constant. We introduce a scheme independent $Λ_{\rm QCD}$ using a connection on the space of the coupling constant.

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arXiv1994

Geometrical Expression for Short-Distance Singularities in Field Theory

We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short distance singularities of the composite fields in terms of beta functions, anomalous dimensions, and a connection. (Based upon a talk given at the International Colloquim on Modern Quantum Field Theory, 5--11 January 1994, Bombay, India.)

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arXiv1994

Operator Product Expansions in the Two-Dimensional O(N) Non-Linear Sigma Model

The short-distance singularity of the product of a composite scalar field that deforms a field theory and an arbitrary composite field can be expressed geometrically by the beta functions, anomalous dimensions, and a connection on the theory space. Using this relation, we compute the connection perturbatively for the O(N) non-linear sigma model in two dimensions. We show that the connection becomes free of singularities at zero temperature only if we normalize the composite fields so that their correlation functions have well-defined limits at zero temperature.

hep-th↗
arXiv1993

Connection on the theory space

By studying the geometric properties of correlation functions on the theory space, we are naturally led to a connection for the infinite dimensional vector bundle of composite fields over the theory space. We show how the short distance singularities of the theory are determined by the geometry of the theory space, i.e., the connection, beta functions, and anomalous dimensions. (This is a summary of the talk given at Strings '93 in Berkeley. The unnecessary blank lines in the original version have been removed in this revised version.)

hep-th↗
arXiv1992

Current-Current Singularities under External Gauge Fields

We study the operator product expansion of two non-interacting chiral currents in the presence of external gauge fields in four dimensional euclidean space. We obtain the operator singularity in terms of the beta function of the free energy density and a connection on the space of external gauge fields, by imposing the consistency between the variational formula, introduced previously by the author, and both the renormalization group equations and the equation of motion for the currents. As a byproduct, we derive a euclidean version of the anomalous commutator of two currents in an appendix.

hep-th↗
arXiv1992

Composite Operators in QCD

We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is given as spatial integration of the operator conjugate to a parameter. The operator product of a composite operator and a conjugate operator has an unintegrable part, and the formula requires divergent subtractions. By imposing consistency conditions we derive a relation between the anomalous dimensions of the composite operators and the unintegrable part of the operator product coefficients.

hep-th↗
arXiv1992

Operator Coefficients for Composite Operators in the $(ϕ^4)_4$ Theory

In a previous paper we derived a relation between the operator product coefficients and anomalous dimensions. We explore this relation in the $(ϕ^4)_4$ theory and compute the coefficient functions in the products of $ϕ^2$ and $ϕ^4$ to first order in the parameter $λ$. The calculation results in two-loop beta functions.

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