Infinite-component fields as a basis for a finite quantum field theory

A quantum field theory based on infinite-component fields is developed in which the spectrum of particles for all spins is composed of infinite sums of finite, non-unitary representations of the Lorentz group. This leads to a field theory free of causality problems. The problem of gauging away all unphysical modes in the infinite-component field theory is achieved by using infinite-parameter gauge fields which remove all unphysical modes, independently of the number of space-time dimensions. A model of an infinite-component quantum field theory is formulated, using perturbation theory, in which there are no ultraviolet divergences and the S-matrix is causal and unitary.     

Infrared finite S-matrix in the QCD coherent state basis

The infrared (IR) structure of the S-matrix in the basis of the QCD coherent states is studied. To any order perturbation theory it is shown that these matrix elements areIR finite in spite of the fact that they involve any number of soft gluons; moreover, these soft gluons do not even contribute to the IR singular part of the inclusive Bloch-Nordsieck distribution. Finally, the BRS charge related to the coherent state S-matrix elements is given and shown to be IR finite to any order perturbation theory.     

Perturbation theory with higher derivative couplings

The formalism of partial differential equations with respect to coupling constants is used to develop a covariant perturbation theory for the interpolating fields and theS matrix when the coupling terms in the Larangian density involve arbitrary (first and higher) derivatives. Through the notion of pure noncovariant contractions, the free-fieldT and the (covariant)T ^* products can be related to each other, allowing us to avoid the Hamiltonian density altogether when dealing with theS matrix. The important ingredients in our approach are (1) the adiabatic switching on and off of the interactions in the infinite past and future, respectively, and (2) the vanishing of four-dimensional delta functions and their derivatives at zero space-time points. The latter ingredient is a prerequisite that our formalism and the canonical formalism be consistent with each other, and on the other hand, it is supported by the dimensional regularization. Corresponding to any Lagrangian, the generalized interaction Hamiltonian density is defined from the covariantS matrix with the help of the pure noncovariant contractions. This interaction Hamiltonian density reduces to the usual one when the Lagrangian density depends on just first derivatives and when the usual canonical formalism can be applied.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Hidden symmetry of the two-dimensional chiral fields

We examine the non-Abelian Goldstone boson (chiral field) interaction in two dimensions. As was shown earlier, this theory strongly resembles the Yang-Mills theory in four dimensions. It is shown that dynamics of chiral fields is governed by the infinite number of the non-trivial conservation laws, which impose strong limitations on the S matrix.     

Extended electron and nonlocal electromagnetic interaction: The perturbation theory

The nonlocal interaction between electrons and electromagnetic fields is considered. It is shown that different contraction forms of interacting fields are equivalent to different nonlocal theories where nonlocality is connected to either the photon field or the electron field, or to both these fields simultaneously. The nonlocal theory where the electron carries nonlocality is studied in detail. The gauge invariance of this model is achieved by using thed-operation applying the perturbation theory. Primitive Feynman diagrams of the nonlocal theory are investigated and a restriction on the “size”l of the electron is obtained. From low-energy experimental data from tests of local quantum electrodynamics it follows thatl≦10⁻¹⁵ cm.     

Infrared problems in quantum electrodynamics

We present a self-contained treatment of the infrared problem in Quantum Electrodynamics. Our program includes a derivation and proof of finiteness of modified reduction formulae for scattering in Coulomb potentials and unitary extensions of the relativistic Coulomb amplitudes in the forward direction. The renormalization structure of the theory is discussed in connection with the infrared problem and the renormalization group is reconsidered and shown to be inadequate for the “improvement” of perturbation theoretic results. However, simple forms of the renormalization group equations are easily established, which allow for a simple discussion of the renormalization structure and the extraction of physical quantities out of Green functions normalized at an arbitrary mass μ < m (m is the fermion mass). As an example of such a quantity we consider the construction of a renormalized and infrared finite mass-operator in presence of external fields. Scattering theory in Quantum Electrodynamics is elaborated in the context of the coherent state formulation of the asymptotic condition. Dimensional regularization techniques are systematically used for the reduction of coherent states and the construction of S-matrix elements and the cross-section formulae. The latter are obtained in a relatively simple form, which allows for a direct comparison with the exact cross-section formulae derived in the traditional context. This establishes the equivalence of the two approaches at the cross-section level. Various applications illustrate the techniques presented here and relative topics are discussed.     

Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG⁺ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary S matrix, and find that it coincides with the one proposed by Bajnok, Palla and Takács for the Dirichlet BSSG⁺ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary S matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.     

Bounded perturbations of the P(ϕ)2 theory

As a perturbation to the P(?)₂ theory we consider interaction densities of the form V(?(x)), where ?(x) is a scalar hermitian boson field and V(α) is a bounded real continuous function. It is proved that the asymptotic fields exist and are equal to the asymptotic fields of the P(?)₂ theory. The connection with non-polynomial theories of rational type is indicated. Furthermore the consequences of a bounded perturbation for the S-matrix and the spectral properties are discussed.     

Hamiltonian reduction of SU(2) gluodynamics

The Hamiltonian reduction of the Yang-Mills theory with the structure group SU(2) to a nonlocal model of a self-interacting 3 × 3 positive semidefinite matrix field is presented. Analysis of the field transformation properties under the action of the Poincaré group is carried out. It is shown that, in the strong coupling limit, the classical dynamics of a reduced system can be described by the local theory of interacting nonrelativistic spin-0 and spin-2 fields. A perturbation theory in powers of the inverse coupling constant g ^−2/3 that allows calculating the corrections to a leading long-wave approximation is suggested.     

Finite size effects and spontaneously broken symmetries: the case of theO(4) model

Finite volume numerical simulations of scalar models with continuous symmetry face strong finite size effects in the broken phase due to the presence of light Goldstone states. In the region where the light Goldstone bosons dominate the dynamics of the system universal finite size scaling formulae are predicted by chiral perturbation theory. Introducing a finite external source one can determine infinite volume, zero external source physical quantities from finite volume observables. Here we apply this theoretically controlled approach to the 4 dimensionalO(4) scalar model. All of our numerical results are in excellent agreement with the predicted finite size scaling forms. We confirm earlier results at zero external source where the infinite volume limit was approximated by projecting the fields to the direction of the magnetization.     

The size of finite size effects in lattice gauge theories

If a quantum field is enclosed in a spatial box of finite volume, its mass spectrum depends on the box size L. For field theories in the continuum Lüscher has shown to all orders in perturbation theory that for large L this dependence is related to certain scattering amplitudes of the infinite volume theory. We derived the corresponding relations for lattice field theories. Assuming their validity for lattice gauge theory outside the perturbative region the magnitude of finite size effects on the spectrum is determined by a glueball coupling constant. This quantity is estimated by strong coupling methods.     

Conformal off-mass-shell extension and elimination of conformal anomalies in quantum gravity

Radiative corrections in the Einstein quantum gravity are made manifestly conformally invariant without changing the S matrix. The conformally invariant form of the classical gravitational action is restored. It is shown, that conformal anomalies, discovered in gravitating systems, do not affect the S matrix. Off the mass shell these anomalies are eliminated by the appropriate choice of a regularization.     

Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

An extension of the coupled cluster formalism to excited states (I)

The expS method (coupled cluster formalism) is extended to excited states of finite and infinite systems. We obtain equations which are formally similar to the known ground-state equations of the expS theory. The method is applicable to Fermi as well as Bose systems.     

Asymptotic perturbation expansion in theP(φ)2 quantum field theory

In theP(φ)₂ model it is proved that the perturbation series for the infinite volume Schwinger functionsS(λ) are asymptotic in the limit as the coupling constant λ goes to zero. We also give conditions which imply smoothness ofS(λ) at arbitrary λ.