Boson Self-interactions Research Articles

Strong high-energy scattering in theories with weak coupling.

The problem of the existence of strong nonperturbative scattering at high energy in theories with weak coupling is considered. It is shown that such scattering associated with multiboson production definitely exists in practically any theory with self-interacting bosons. An approach to this problem is proposed which is based on explicit splitting of the short-wave and the long-wave modes of the bosonic field and considering the process of excitation by the initial particles of the long-wave field to states with large energy. The nonperturbative analysis of the probability of excitation of the soft field to a large amplitude is based on the WKB technique developed in quantum mechanics for similar problems. It is also shown that the results of previous calculations can be reproduced within the proposed approach including those based on the analysis of instanton-induced amplitudes.

The cosmological formation of boson stars

The formation of boson stars by gravitational collapse in the early universe is considered. It is demonstrated that while the simplest models are unfavourable for boson star formation, the inclusion of a boson self-interaction and consideration of a boson-antiboson asymmetry allow substantial possibilities for the cosmological formation of boson stars.

Phenomenological implications of an electroweak theory without Higgs

An alternative to the standard electroweak gauge theory is considered which does not involve the physical Higgs particle, but contains heavy vector boson resonances manifesting the strong gauge boson self-interactions. We investigate phenomenological implications of such a theory and demonstrate that processes including heavy quarks (in particular heavy quark pair production and asymmetry in e +e − annihilation) constitute a good testing ground for experimentally discriminating this theory from the SM at energies available at present or within the near future.

Vector boson scattering ate + e − colliders as a test ofW ±,Z 0, γ self-interactions

We investigate the potential of a high-energye+e− collider (e.g., CLIC,E e +=E e −=1 TeV) for determining trilinear and quadrilinear vector boson self-interactions in various vector boson scattering processes which can be measured in reactions of the type\(e^ + e^ - \to (e^ + e^ - ,ve^ - ,\bar ve^ + ,v\bar v) + VV'\). Our analysis is based upon a recently suggested single parameter Lagrangian model for vector boson self-interactions incorporating globalSU(2) weak isospin symmetry broken by electromagnetism and a minimal increase of vector boson scattering tree amplitudes as a function of the energy. The results are compared with theSU(2) L ×U(1) Y predictions for the cases of a light and a heavy Higgs boson. We find that the crosssection for the production of a vector boson pair,VV′, is very sensitively dependent on the magnitude of the single free parameter, κ, the anomalous magnetic dipole moment of theW±. The cross-section changes by approximately one order of magnitude, even near production threshold, if κ is varied by one unit around theSU(2) L ×U(1) Y value of κ=1.

Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation.

This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ scalar fields in flat space. We adopt the closed-time-path (CTP or ``in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming a thermal distribution we recover the real-time finite-temperature theory as a special case. By requiring the CTP effective action to be stationary with respect to variations of the correlation functions we obtain an infinite set of coupled equations which is the quantum-field-theoretical generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Truncation of this series leads to dissipative characteristics in the subsystem. In this context we discuss the nature of dissipation in interacting quantum fields.To one-loop order in a perturbative expansion of the CTP effective action, the 2PI formalism yields results equivalent to the leading 1/N expansion for an O(N)-symmetric scalar field. To higher-loop order we introduce a two-time approximation to separate the quantum-field effects of radiative correction and renormalization from the statistical-kinetic effects of collisions and relaxation. In the weak-coupling quasiuniform limit, the system of nonequilibrium quantum fields can subscribe to a kinetic theory description wherein the propagators are represented in terms of relativistic Wigner distribution functions. From a two-loop calculation we derive the Boltzmann equation for the distribution function and the gap equation for the effective mass of the quasiparticles. One can define an entropy function for the quantum gas of quasiparticles which satisfies the H theorem. We also calculate the limits to the validity of the binary collision approximation from a three-loop analysis. The theoretical framework established here can be generalized to nonconstant background fields and for curved spacetimes.

On W±, Z0, γ self-interactions

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s 2 ) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W ± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2) L × U(1) Y theory for m H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2) L × U(1) Y electroweak theory in processes such as e + e − → W + W − .

Non-standard self-interactions of the weak vector bosons and their phenomenological implications

Based upon the parts of the standard electroweak model which have been verified by experiment so far, a generalization into the sector of the weak vector boson self-interactions is undertaken. The guiding principles are dimensionless couplings, electromagnetic gauge invariance and a global SU(2) WI symmetry. The consequences of this general approach for the phenomenology at the future colliders of high center of mass energy (LEP, Tevatron, SSC) are discussed in detail. The general approach encompasses the standard model as a special case and therefore our discussion is useful as well for a synoptic view of the tests of the self-interaction part of the standard model.

Global-operator perturbation theory for a self-interacting boson system

We consider a single-mode self-interacting boson system with an arbitrary interaction. The Van Vleck-Primas operator perturbation theory can be used to obtain the perturbative solutions to any desired order in closed form. In contrast to ordinary perturbation theory, which deals with each state individually, the present method is global and treats all the states in the spectrum collectively. The solution process involves the systematic application of four basic rules.

Analytic and numerical evidence from quantum field theory for the hyperscaling relation dv = 2??? in the d=3 ising model

The hyperscaling relationdv = 2Δ - γ(d=3) for the Ising model has been shown to follow from a constructive approach proposed by one of the authors (R.S.) of a relativistic theory of self-interacting Bosons in d space-time dimensions. We present evidence that the two assumptions made in this approach are valid: On a finite Euclidean (hyper-) cubical lattice in d dimensions the renormalization map from the bare to the renormalized parameters should have nonvanishing Jacobian everywhere. We show this analytically and numerically on the boundary set of the parameters. The numerical analysis involves Monte Carlo calculations in the region where the bare coupling constantg 0 is infinite, giving the Ising model. The linear sizen of the lattice (with periodic boundary conditions) was taken to be 5, 6, and 10. There we also checked the second assumption saying that the correlation length for the Ising model is a monotonic function of the temperature. We also comment on the possible numbers of zeros of the Callan-Symanzikβ function of this theory.

Classical source emitting self-interacting bosons

A general expression is derived for the $S$-matrix elements for a self-interacting boson field in interaction with a classical current. The probability for the emission of boson radiation up to a certain total energy is determined, and it is shown how infrared divergences are canceled or reduced. The formal extension by functional methods to a quantum current is indicated.

Bound states and solitons in the Gross-Neveu model

The results for the spectrum of bound states and of solitons first deduced by Dashen, Hasslacher, and Neveu for a model of interacting fermions by techniques of functional integration are obtained here by methods based on Heisenberg field mechanics analogous to those applied previously to models of self-interacting bosons. The method of solution is suggested by a simplified physical picture of the bound states: These are computed in a Hartree approximation in which the self-consistent potential is a sum of contributions from the fermions (and antifermions) occupying orbitals in the conventional many-body picture and from the vacuum fluctuations of single-closed-loop type. In the same approximation the self-consistent field generated by the heavy soliton is a result of the vacuum fluctuations alone. As the main new technical contribution, we deduce and solve directly equations determining the self-consistent fields as well as the amplitudes ("wave functions") from which these are constructed. We comment on the degeneracy of the heavy soliton state.

Self-interacting, boson, quantum, field theory and the thermodynamic limit in d dimensions

By use of a finite volume, lattice approximation, we set up an approximation to the analytic continuation of a polynomial, self-interacting boson quantum field theory from Minkowski space to Euclidean space. The infinite volume limit for various boundary conditions is shown to exist and to be asymptotic to the perturbation expansion in the coupling constant g at g=0. For g:φ4:d theory we prove mass renormalizability and show how, by use of Nelson’s reconstruction theorem, the corresponding Minkowski space quantum field theory can be obtained. We discuss, at least for d?4, how statistical mechanical techniques, used to analyze the Ising model in the critical region just above the critical temperature, can be used to compute the properties of quantum field theory.

S matrix in constructive quantum field theory

An investigation is made of the equations for the coefficient functions of the S matrix for the example of a self-interacting boson field in two-dimensional spacetime. The methods of constructive quantum field theory are used to show that the perturbation series in the limit of infinite volume can be regarded as an asymptotic series in the sense of weak convergence. A new approach is proposed to the investigation of the equations for the coefficient functions of the S matrix in infinite volume in a Hilbert space of translationally invariant functions. The existence of a solution of some approximate equations is proved.

Nonperturbative effective potential forλφ4theory in the many-field limit

A $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory of self-interacting boson fields with $\mathrm{O}(N)$ symmetry is considered. A nonperturbative method is developed to compute the effective potential, which becomes exact in the large-$N$ limit. The stability of the vacuum and possible spontaneous symmetry breakdown of the theory are studied in this limit. The existence of a local mimimum requires $0l1+{(N\ensuremath{\lambda})}^{\ensuremath{-}1}96{\ensuremath{\pi}}^{2}$, which may be either a true bound or an indication of the breakdown of the ${N}^{\ensuremath{-}1}$ expansion. The function $\ensuremath{\beta}(\ensuremath{\lambda})$ that appears in the Callan-Symanzik equations is calculated in the large-$N$ limit of the massless theory without reference to a perturbation expansion in $\ensuremath{\lambda}$. It is observed that the presence of a nontrivial zero of $\ensuremath{\beta}(\ensuremath{\lambda})$ is a necessary condition for a spontaneously broken symmetry in the massless theory. On this basis, it is shown that this $\ensuremath{\beta}(\ensuremath{\lambda})$ is unlikely to have a nontrivial zero. The leading-logarithm approximation to the effective potential is discussed within the above framework.

On the renormalization method: a different outlook, and the energy-momentum tensor in the gφ4 theory

An alternate method of renormalizing a quartic self-interacting boson theory has been developed. We find that one can obtain finite renormalized expressions for the perturbation theory contributions to the Green's function without carrying out limiting procedures. As a consequence of the analysis, one is able to renormalize explicitly the field energy-momentum tensor to all orders. There exists a one-parameter family of renormalized tensors. The method will allow for a simple determination of the asymptotic “zero-mass” theory.

On the Feynman rules for chiral interactions

The steps necessary to set up a perturbation theory for the chiral invariant self-interaction of massless bosons are considered. One can decide what the canonical procedures give and then, wherever possible, replace the canonical procedures by the more naive Feynman rules and see what compensation has to be introduced into the interaction. The procedure starts with the ordered hamiltonian given by Charap, its use is equivalent to the use of the expected (-Lint) term, but modified by two singular terms. The first, being proportional to delta 4(0), is well known. The second, proportional to ( delta 3(0))2, comes from the correct use of Wick's theorem with our specified ordering. Normal ordering cannot be used to remove tadpole contributions though this is not because the required normal ordering violates the chiral invariance. It is a characteristic of any such self-interaction theories and therefore has important consequences for many superpropagator calculations.

A general class of quantum fields without cut-offs in two space-time dimensions

We consider a selfinteracting boson field in two space-time dimensions, with interaction densities of the form:V(ϕ(x)): where ϕ(x) is a scalar boson field, andV(α) is a real positive function of exponential type. We define the space cut-off interaction by $$V_r = \int\limits_{\left| x \right| \leqq r} {:V(\varphi (x))} :dx$$ and prove thatH r =H 0+V r , whereH 0 is the free energy, is essentially self adjoint. This permits us to take away the space cut-off and we obtain a quantum field free of cut-offs.

A remark on Yukawa plus boson selfinteraction in two space time dimensions

In this note we show how the results of Glimm and Jaffe [5, 6] on the Yukawa quantum field theory in two space time dimensions may be extended to the case where a boson selfinteraction term is added. Local fields are constructed which do not depend on any cut-off and which have the right (anti)-commutation properties for spacelike separated support of the test functions.

Energy-Momentum Spectrum and Vacuum Expectation Values in Quantum Field Theory

We consider nonlinear boson self-interactions with a periodic spatial cutoff. We prove that the energy-momentum spectrum lies in the forward light cone. A momentum cutoff does not influence this result. For theories with finite-field strength renormalization, we obtain bounds on the vacuum expectation values of products of the φt's and ∇φ's. These bounds are uniform in the volume (and possible momentum) cutoff.

A λφ2n field theory without cutoffs

We consider a self-interacting scalar boson field in two-dimensional space-time with self-interaction given by an arbitrary Wick polynomial of even degree in the field. It is shown that the field theory can be constructed in a Hilbert space of physical states. The hamiltonian is a positive self-adjoint operator possessing a physical vacuum. The method of proof consists of imposing and then removing three cutoffs: a box cutoff, an ultraviolet cutoff, and a space cutoff. As the first two are removed the resolvents of the cutoff hamiltonians converge uniformly and this leads to the self-adjointness of the spatially cutoff hamiltonian.