Spinless Fields Research Articles

D = 11 supergravity with local SU(8) invariance

The transformation rules and field equations of d = 11 supergravity are given in a form which is manifestly covariant under local SU(8) transformations. In this formulation the SO(1, 10) local Lorentz group is replaced by SO(1, 3) × SU(8). The spinless fields are described by covariant quantities which constitute the 56 and 133 representations of E 7(+7).

Zero-point field in curved spaces.

Boyer's conjecture that the thermal effects of acceleration are manifestations of the zero-point field is further investigated within the context of quantum field theory in curved spaces. The energy-momentum current for a spinless field is defined rigorously and used as the basis for investigating the energy density observed in a noninertial frame. The following examples are considered: (i) uniformly accelerated observers, (ii) two-dimensional Schwarzschild black holes, (iii) the Einstein universe. The energy spectra which have been previously calculated appear in the present formalism as an additional contribution to the energy of the zero-point field, but particle creation does not occur. It is suggested that the radiation produced by gravitational fields or by acceleration is a manifestation of the zero-point field and of the same nature (whether real or virtual).

Dynamical implementation of mass hierarchies and gauge boson coupling constants

Conventional mass consistency equations of Nambu-Jona-Lasinio-type cannot produce hierarchical mass ratio—even if the ultraviolet divergences are cured in some way. This is in contrast with the theory of superconductivity where—via logarithms—such mass hierarchies are quite natural. We propose—in analogy to superconductivity—a modification of the singularity structure of the fermions which lead, by their self-interaction, to a symmetry breakdown. The arising ghostlike fermions —which seem to establish an alternative to the algebraic technifermion picture—allow the build-up of composite gauge bosons. In analogy to the unitarization procedure for non-Abelian gauge bosons with anticommuting spinless fields, we propose—explicitly on the one-loop level—a unitarization formalism also for the ghostlike subfermions by employing commuting spin-1/2 fields. There arises a close connection between the mass characterizing the symmetry breakdown and the value of the gauge boson coupling constant.

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.

Quantum field theories on a lattice: Variational methods for arbitrary coupling strengths and the Ising model in a transverse magnetic field

This paper continues our studies of quantum field theories on a lattice. We develop techniques for computing the low-lying spectrum of a lattice Hamiltonian using a variational approach, without recourse either to weak- or strong-coupling expansions. Our variational methods, which are relatively simple and straightforward, are applied to the Ising model in a transverse magnetic field as well as to a free spinless field theory. We demonstrate their accuracy in the vicinity of a phase transition for the Ising model by comparing with known exact solutions.

Some static solutions of the massless λϕ 4 theory

Some state configurations for a classical spinless and massless field are here presented and discussed. They are solutions of the equations Δϕ-λϕ3=0. Some excitations of those configuration are briefly 3 discussed.

The Bogoliubov Transformation in the Field Theory

It is confirmed that the method of the Bogoliubov transformation is applicable also in the field theory. The original representation suited for a massless spinor field, ψ(0), can be transformed into another representation, in which the spinor field has a non-zero mass, for the Fermi interactions of any type, by the transformation. But the interaction responsible for the finite mass is the scalar part of the interaction itself or of the equivalent expression obtained by the Fierz transformation. As to the Yukawa interaction, the Bogoliubov transformation must be accompanied by a linear transformation for the Bose field, and the combined transformation is meaningful only for the scalar coupling of a scalar meson with mass. The situation about the φ4 interactions of spinless fields φ is completely the same as in the case of the Fermi interaction, but the method is not applicable to the φ3 interaction of a scalar field. Thus it is suggested that the quantities <<:ψ(0)ψ(0):>> for the Fermi interaction, <<φ(0)>> for the Yukawa interaction, and <<:φ(0)2:>> for the φ4 interactions correspond to the parameter of the long range order in the theory of superconductivity, respectively, where the notatin << >> means the expectation value in the transformed vacuum. It is also shown that Lehmann's method of the spectrum representation can be generalized to treat the canonical transformation, and that it gives a covariant and convenient method to derive the mass equation. In the last section, it is discussed what kinds of image of assumption must be introduced in order that the representation obtained by the Bogoliubov transformation can be used to the unified theories of elementary particles. Counter-examples to the too conventional method used in the theories of spontaneous breakdown of symmetries are also exhibited (§5 and App. I).

Field Theory of Matter

A speculative field theory of matter is developed. Simple computational methods are used in a preliminary survey of its consequences. The theory exploits the known properties of leptons by means of a principle of symmetry between electrical and nucleonic charge. There are fundamental fields with spins 0, \textonehalf{}, 1. The spinless field is neutral. Spin \textonehalf{} and 1 fields can carry both electrical and nucleonic charge. The multiplicity of any nonzero charge is 3. Explicit dynamical mechanisms for the breakdown of unitary symmetry and for the muon-electron mass difference are given. A more general view of lepton properties is proposed. Mass relations for baryon and meson multiplets are derived, together with approximate couplings among the multiplets. The weakness of $\ensuremath{\varphi}$ production in $\ensuremath{\pi}\ensuremath{-}N$ collisions and the suppression of the $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\rho}+\ensuremath{\pi}$ decay is explained.

Some Consequences of Gauge Invariance

A simple theorem is .,rated to expand the matrix element Jor a process concerning any number of photons or external elecrrpmagnetic fields into the independent gauge invariant terms. It turns out 'hat the number of such terms is uniquely determined by the initial and final states of the process, regardless of the intermediate states and the type of iqteraction. We have, for example, 4, 14, and 10 independent gauge invariant terms (or the production Qf spin 0 and 1 mesons bv photons . and the Compton scattering, respectively. Some of the well-known absolute selection {ulesfor meson decays can be also derived from this gauge invariant expansion theorem. In their recent works on the production of spinless mesons by photons,')'** Kobaet al. have shown that the requirement of gauge invariance greatly simplified the evaluation and made facile the analysis of the results. In fact they developed. the enormous number of matrix elements into only four independent gauge invariant terms irrespective of the order of approximation. Their conclusion was a direct consequence of i) Lorentz invariance, ii) gaugeinvariance, iii) energy-momentum conservation, iv) spinless field for the meson, and v) Dirac equation for the nucleon, and thus it mattered only about the initial and final states of the process but not about the method of calculation. Such a procedure can therefore be applied 11tlttatis 1nutandis to other cases involving one or more pltotons or external electromagnetic fields. However, since their method itself is very special and seems inconvenient to apply to other processes, its reexamination is desirable. It is the aim of this paper to observe the gauge invariance from the most general points of view and present a method to expand complex matrix elements into their fundamental gauge invariant terms. We shall show in § 2 that a simple consideration indeed a:ffords us such a prescription which is far more concise than theirs· and in addition widely applicable. In the next section, the gauge invariant expansion theorem of the matrix elements is given, according to which it turns out that the number of gauge invariant terms is unambiguously determined by the process, not depending on the method of calculation. We have, for example, 4, 14, and 10 such terms for the production of spin 0 and 1 mesons by photons and the Compton scattering, respectively. In § 4 the possibilities are discussed for utilizing this theorem to derive the absolute selection rules for meson decay. However, as might be expected, the selection rules are obtained only for certain simple cases.