Finite N=1 SUSY field theories and dimensional regularization

A simple algorithm is proposed to construct finite N=1 SUSY field theories within dimensional regularization. This is achieved by choosing the Yukawa couplings to be y_i=g(αⁱ₀+αⁱ₀ϵ+ϵ+αⁱ₂ϵ²+…), where g is the gauge coupling and the coefficients αⁱ₀, αⁱ₁, etc., are calculated order by order of perturbation theory. It is shown that the theory can be made finite in all orders of perturbation theory.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Smooth massless limit of field theories. II

It is shown that the massless limit of any Fierz-Pauli field theory, in the external source approximation, is smooth under certain conditions on the sources. These conditions are no stronger than those that arise from the internal consistency of the massless field theory.     

静电场问题中的微扰方法

把微扰方法应用到电磁理论中,导出了近均匀和近各向同性介质中静电场问题的微扰近似解.     

Thermodynamic calculations in relativistic finite-temperature quantum field theories

A Minkowski space formalism of finite-temperature quantum field theory is used to compute static thermodynamic quantities in the one- and two-loop approximation in an elegant and straightforward way using a generalization of Weinberg's tadpole method of calculating effective potentials. Systematic diagrammatic techniques for low- and high-temperature expansions are developed. Renormalizability by zero-temperature symmetric counterterms is proven for all orders in the loop expansion and demonstrated explicitly to two loops. Many useful computational techniques applicable to general finite temperature calculations are explained.     

Infinite dimensional groups and Riemann surface field theories

We show how to obtain positive energy representations of the groupG of smooth maps from a union of circles toU(N) from geometric data associated with a Riemann surface having these circles as boundary. Using covering spaces we can reduce to the case whereN=1. Then our main result shows that Mackey induction may be applied and yields representations of the connected component of the identity ofG which have the form of a Fock representation of an infinite dimensional Heisenberg group tensored with a finite dimensional representation of a subgroup isomorphic to the first cohomology group of the surface obtained by capping the boundary circles with discs. We give geometric sufficient conditions for the correlation functions to be positive definite and derive explicit formulae for them and for the vacuum (or cyclic) vector. (This gives a geometric construction of correlation functions which had been obtained earlier using tau functions.) By choosing particular functions inG with non-zero winding numbers on the boundary we obtain analogues of vertex operators described by Segal in the genus zero case. These special elements ofG (which have a simple interpretation in terms of function theory on theRiemann surface) approximate fermion (or Clifford algebra) operators. They enable a rigorous derivation of a form of boson-fermion correspondence in the sense that we construct generators of a Clifford algebra from the unitaries representing these elements ofG.     

Sewing conformal field theories II

We show that any Riemann surface M with punctures can be constructed by sewing three-punctured speres. Correspondingly, any correlation function on M can be obtained by sewing three-point functions on a sphere. There is no unique way of sewing three-punctured spheres to construct M, and the resulting correlation functions may depend on the precise way of sewing. We show that this dependence is absent, if we assume that four-point correlation function on a sphere and one-point functions on a torus are determined unambiguously.     

Cancellation of infrared and collinear singularities in relativistic thermal field theories (II)

We study the infrared and collinear divergences of a renormalizable scalar field theory at finite temperature. We give the final results of an investigation undertaken in a previous work by showing the complete cancellation of all divergences at two-loop order in a physical process. This result makes the validity of the Kinoshita-Lee-Nauenberg theorem at finite temperature extremely plausible.     

Existence of quantum soliton forφ 6-like field theories in 1 + 1 dimensions

We reexamine the recent claim that the soliton of the 1 + 1 dimensional field theories does not survive quantum corrections if the adjacent minima of the potential do not have same curvature and show that it is in fact possible to choose counter terms such that the quantum correction to the soliton mass is finite.     

The use of hyperfunctions for radiation reaction calculations in classical field theories

It is shown that the use of hyperfunctions in classical field-theoretical calculations of radiation reaction terms leads to calculational simplifications. No analytic continuation is necessary. The calculation of electromagnetic radiation reaction terms is done as an example. The extension of hyperfunction techniques to general relativity and Yang-Mills fields is discussed.     

Applying the variational principle to (1+1)-dimensional quantum field theories

We extend the recently introduced continuous matrix product state variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the application of the variational procedure to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free of fermion doubling and sign problems. We illustrate the power of the formalism by studying the momentum occupation for free massive Dirac fermions and the chiral symmetry breaking in the Gross-Neveu model.     

Modular invariance and the spectrum of two dimensional conformal field theories

Modular invariance has recently emerged as a powerful tool in conformal field theory. In conjunction with the representation theory of infinite dimensional Lie algebras, the study of modular invariance gave the spectrum of several families of theories. These include the minimal conformal models (Cardy and others), WZW theories which describe string propagation on group manifolds (Gepner and Witten) and parafermionic field theories (Gepner and Qiu). The minimal conformal models models were shown to be a product of two SU(2) WZW theories (Gepner). These results represent a step towards a complete classification of conformal field theories, an important goal both for the study of critical phenomena and string theory.