Infra-red asymptotic behaviour of the one-fermion green's function in a scalar model with isospin

In a theory where massive fermions interact with a massless scalar field of isospin 1, the behaviour of the one-fermion Green's function is found to differ from the free Green's function by a factor $\text{(1 ? (2g}{}^2\text{/π}{}^2\text{)1}\text{n}\text{m|x ? y|)}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>8</mtext>}}$, in the limit of large separation |x ? y|.     

Perturbation theory with instantons

We develop “perturbation theory” rules for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the “dilute gas” approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form where b is the coefficient in the expansion of the β function: β = bg³ + 3. .     

The S-matrix of the kinks of the (gyψ)2 model

We consider the particle-kink and kink-kink S-matrix elements of the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model, where the Majorana spinor ψ is an O(N) isovector. Our results confirm many qualitative ideas about the model, including the mass spectrum, the decoupling at N = 4, and the isospinor nature of the kinks.     

Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.     

Nonrelativistic distorted wave born approximation predictions for 500 MeV (p, p') spin-rotation observables

We discuss couplings of scalar gluonium σ on the basis of the low energy theorems of broken chiral symmetry and the anomalous trace of the energy—momentum tensor, implemented using a phenomenological lagrangian. Taking the ITEP value of the gluon consensate as input, we find $\text{Γ(σ → ππ) ? 0.6}\text{GeV}\text{× (}\text{m}{}_{\mathrm{\sigma }}\text{1}\text{GeV}\text{)}{}^5$ and $\text{Γ(σ → γγ) ? 90}\text{eV}\text{× (}\text{m}{}_{\mathrm{\sigma }}\text{1}\text{GeV}\text{)}{}^5$, while m_σ is undetermined. These results suggest that if the scalar gluonium mass is above 1 GeV, it is probably unobservably wide, while production in γγ collisions is probably too small to be detectable if m_σ < 1.5 GeV. We comment on the observability of J/ψ → σ + γ and on the relevance of our results to other gluonia.     

Supersymmetric pure spinor theory

A theory based solely on a 2×(N=2)-component Weyl spinor field χ(x) of subcanonical dimension $\text{1}\text{2}$ allows the local construction (without derivatives) of effective fermi and bose fields with spins up to N=2. It is demonstrated that the lagrangian $\text{～:}\text{det}\text{xx}{}^1\text{: (x)}$ studied earlier is invariant under a global N=2 supersymmetry transformation and can be cast into a form $\text{～(}\text{det DD}{}^1\text{):ππ}{}^1\text{:}$ involving the scalar chiral superfield $\text{π=}\text{exp}\text{[θ}{}_{\mathrm{x}}\text{(x + iθσθ}{}^1\text{)]}$ the components of which are finite part products of the basic field. The theory can be generalized to an N-supersymmetric theory in a 2N-dimensional space-time yielding the Thirring model as special case for N=1.     

Strong absorption and the distribution of zeros of the S-matrix

The only distributions normally included in a discussion of the statistical theory of nuclear resonance reactions are the distributions of the widths (Γ) and spacings (D) of the levels of the compound nucleus. However, as the usual Hauser-Feshbach theory makes clear, $\text{Γ}$ and $\text{D}$ alone are not sufficient to determine the ratio $\text{σ}{}_{\mathrm{cc\prime }}{}^{\mathrm{<mtext>dir</mtext>}}\text{σ}{}_{\mathrm{cc\prime }}{}^{\mathrm{<mtext>fl</mtext>}}$. In an attempt to determine what further statistical information is sufficient to determine this ratio, in the special limit that it tends to zero for all cc′, c ≠ c′ (the “strong-absorption” limit), we study several “picket fence” S-matrix models, as well as a random-residue model exhibiting Ericson fluctuations. These models indicate that the strong-absorption limit $\text{(}\text{S}{}_{\mathrm{cc\prime }}\text{= 0,}\text{all}\text{cc′)}$ is directly related to the distribution of the zeros of S_cc′(E) in the upper half of the complex E-plane, and that strong absorption is reached only if these zeros are distributed with a high density in the region E → + i ∞. As a by-product, we obtain a generalization of the theorem of Moldauer and Simonius $\text{[|}\text{det}\text{S}\text{| =}\text{exp}\text{(?π}\text{Γ}\text{/}\text{D}\text{)]}$. Our generalization applies to individual optical S-matrix elements (and so to direct-reaction cross sections) rather than just to their determinant.     

K-K mixing in the standard model

We present a new calculation of the B parameter which governs the short distance contribution to the $\text{K}{}^0\text{-}\text{K}{}^0$ off-diagonal mass matrix. The calculation combines the information provided by the effective chiral lagrangian realization of QCD at long distances with the perturbative behaviour of QCD at short distances via the local duality approach. The result exhibits an explicit renormalization scale dependence which exactly cancels with the corresponding dependence in the Wilson coefficient.     

Consistent MFA correlation functions of Ising models for all temperatures

A correct calculation of the Ising model correlation function C(q) = 〈(S(q) ? 〈S(q)〉) (S(-q) ? 〈S(-q)〉)〉 in the MFA results in

$\text{C(q)=}\text{〈S}{}^2\text{〉?〈〉}{}^2\text{1?(〈S}{}^2\text{〉?〈S〉}{}^2\text{βJ(q}\text{1}\text{N}\text{∑}\text{q}\text{1}\text{1?〈S〉}{}^2\text{βJ(q)}{}^{\mathrm{?1}}\text{C(q) fulfills the exact sum rule N}{}^{-1}\text{Σ}{}_{\mathrm{q}}\text{C(q) = 〈S}{}^2\text{〉 ? 〈S〉}{}^2$

. Previous literature supposed a violation of this sum rule to be a characteristic disadvantage of this approximation.     

General theory of virtual heavy-particle effects in renormalizable field theories (I)

We develop a systematic method of isolating the effects of virtual heavy particles in renormalizable field theories. With a φ⁴-type field-theory model involving two real scalar fields (one with a heavy mass M, and the other light), we show in detail, that up to order $\text{1}\text{M}{}^2$ (but to all orders in renormalized coupling), effects of virtual heavy particles can be completely incorporated into pure light-particle theory via effective local vertices which involve operators of canonical dimension at most six. All the coupling strengths for such effective local interactions are of order $\text{1}\text{M}{}^2$ (the decoupling theorem) and are systematically calculable in renormalized perturbation theory. We also derive a closed set of Callan-Symanzik equations which are satisfied by these coupling strengths. Using these equations, we explicitly sum all the leading logarithms (i.e., log M ～ O(1)) which appear in the perturbative calculations of the effective coupling strengths.     

A mechanism for quark confinement

Euclidean field configurations carrying half integral topological charge, merons, can, unlike ordinary instantons, confine quarks at moderate coupling g. Logarithmic interactions between merons prevent isolated ones from existing for small g. However, in four dimensional QCD a crude calculation indicates a phase transition to a quark confining plasma at an effective coupling $\text{g}{}^2\text{4π}{}^2\text{≈}\text{1}\text{4}$.     

Exact quantum Sine-Gordon soliton form factors

Soliton form factors are constructed using Zamolodchikov's proposed exact massive Thirring model S-matrix. The asymptotic behaviour of the electromagnetic form factor is $\text{～(?t)}{}^{\mathrm{<mtext>?</mtext><mtext>g</mtext><mtext>2</mtext>}}$. The quasiclassical limit is not the previously accepted result.     

Search for sleptons and squarks at the Z0 peak in e-e+ colliders

We investigate single scalar lepton and scalar quark production processes $\text{e}{}^{\mathrm{-}}\text{e}{}^{\mathrm{+}}\text{→ Z}{}^0\text{→}\text{?}{}^{\mathrm{\pm }}\text{γ}\text{?}{}^{\mathrm{\pm }}\text{,}\text{q}\text{γ}\text{q}\text{and}\text{q}\text{g}\text{q}$ at the Z⁰ peak. We find that a detectable number of these scalars should be produced at the SLC and LEP-I colliders even if their masses substantially exceed the beam energy E = m_Z/2?45 GeV.     

Temperature and thickness dependence of low temperature transport in amorphous silicon thin films: A comparison to amorphous germanium

The temperature and thickness dependence of the low temperature electrical transport of amorphous silicon thin films measured in-situ in ultra-high vacuum are presented. As for a-Ge there is an extended range of $\text{ln ? ∝ T}{}^{\mathrm{<mtext>?1</mtext><mtext>4</mtext>}}$ for thick films with $\text{ln ? ∝ S}{}_2\text{T}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ for thin films with $\text{S}{}_2\text{∝ d}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ as expected from a variable range tunneling mechanism.     

Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

Electromagnetic field in the gauge SU(3) × SU(3) chiral group

The massless electromagnetic Yang-Mills field is explicitly constructed as a linear combination of 16 gauge fields of the chiral SU(3) × SU(3) group within the framework of the plasmon generating mechanism [1]. The remaining 15 gauge fields acquire a mass through the non-zero vacuum expectation values of the auxiliary scalar multiplet which transforms according to the (8,8) representation of the gauge group. The tadpoles with non-zero hypercharge which are required for the existence of the only massless electromagnetic potential A_μ are due to the natural mixing of charged weak currents with ΔS = 0 and ΔS = 1. The relevance of this phenomenon to the Cabibbo angle is briefly discussed. Also presented is a theorem concerning an admissible form of the zero-order mass term of gauge fields when the canonical number is unknown.     

Instantons in conformal gravity

We study extrema of the general conformally invariant action:

$\text{S}{}_{\mathrm{c}}\text{= ∫}\text{1}\text{α}{}^2\text{C}{}^{\mathrm{abcd}}\text{C}{}_{\mathrm{abcd}}\text{+γR}{}^{\mathrm{abcd}}{}^1\text{R}{}_{\mathrm{abcd}}{}^1\text{+iθR}{}^{\mathrm{abcd}}\text{1R}{}_{\mathrm{abcd}}$

.We find the first examples in four dimensions of asymptotically euclidean gravitational instantons. These have arbitrary Euler number and Hirzebruch signature. Some of these instantons represent tunneling between zero-curvature vacua that are not related by small gauge transformations. Others represent tunneling between flat space and topologically non-trivial zero-energy initial data. A general formula for the one-loop determinant is derived in terms of the renormalization group invariant masses, the volume of space-time, the Euler number and the Hirzebruch signature.     

Polyakov's spinning string from canonical point of view

We give a canonical formulation of Polyakov's modified spinning string theory. This means that we start with the lagrangian , where $\text{L}$₁ is a counter term derived from the general form of the trace anomaly. In the superconformal gauge $\text{L}$₁ reduces to the supersymmetric Liouville lagrangian. A general solution of the supersymmetric Liouville equation is derived as well as appropriate boundary condutions for the Neveu-Schwarz (NS) and Ramond models. Under the assumption that the exact quantization of the Liouville theory does not yield any additional anomalies. We show that relativistic invariance requires the constant C to be $\text{C=}\text{10?D}\text{8π}$, in agreement with Polyakov's result. For D<10 the string acquires longitudinal modes. A semiclassical quantization of the Liouville theory is then performed with the result that the mass spectrum starts with $\text{m}{}^2\text{?}\text{1}\text{2}\text{α′}\text{and}\text{m}{}^2\text{= 0}$ in the NS and Ramond models in any dimension D?10. The longitudinal excitations are determined by a simple harmonic oscillator expression. It is shown that a consistent exact quantization could remove the tachyon state in the NS model.     

Light composite fermions in a dynamical subquark model of pregauge interactions

The masses of composite leptons and quarks are discussed in a “dynamical subquark model of pregauge interactions”. In this model, the leptons and quarks are made of a spinor and scalar subquark with equal mass, M, and the gauge bosons and Higgs scalar of the SU(3)_c×SU(2)_L×U(1)_Y model are made of a subquark-antisubquark pair. The SU(2)_L×U(1)_Y symmetry is spontaneously broken by the composite Higgs scalar and the (scalar) subquark mass parameter is in turn bounded as $\text{M > 5.4}\text{TeV}\text{(=2π(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{where}\text{G}{}_{\mathrm{<mtext>F</mtext>}}$ is the Fermi coupling constant). The spontaneously generated mass of a lepton or quark, m_i⁽ⁿ⁾ (i = 1, 2; n = 1 ～ N_g), is calculated to be: $\text{m}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{× (4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)α}{}_{\mathrm{<mtext>e.m.</mtext>}}\text{(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/3}\text{6}\text{(=0.35r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{(4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)}\text{GeV}\text{),}\text{where}\text{r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}$ are the parameters satisfying that 0 ? r_i⁽ⁿ⁾ ? 1 and Σ (r_i⁽ⁿ⁾)² = 1;N_g is the total number of generations of the leptons and quarks; α_e.m. is the fine structure constant. The appearance of light composite fermions is related to a specific mechanism of generating global chiral symmetries of the leptons and quarks. Global symmetries of scalar subquarks yield chiral symmetries of the leptons and quarks. Our model turns out to satisfy 't Hooft's anomaly conditions on massless composite fermions.     

Derivation of the classical theory of correlations in fluids by means of functional differentiation

The k-particle, infinite-volume distribution functions $\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ)}$ and modified Ursell correlation functions $\text{U}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ)}$ of a classical system of particles with the two-body potential $\text{q(}\text{r}\text{) + γ}{}^{\mathrm{\nu }}\text{K(γ}\text{r}\text{)}$ are considered. The limiting values of the functions $\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ),}\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{S}{}_1\text{/γ, …,}\text{S}{}_{\mathrm{k?1}}\text{/γ, γ)}$ and $\text{γ(}{}^{\mathrm{1?k}}\text{)ν}\text{U}\text{?}{}_{\mathrm{k}}\text{(}\text{S}{}_1\text{/γ, …,}\text{S}{}_{\mathrm{k?1}}\text{/γ, γ)}$ in the limit γ → 0 are calculated, under fairly weak conditions on q and K, by a method involving functional differentiation. These limiting functions are used to describe the molecular structure of the various states of the system both in the range of the potential q(r) and in the rage of the potential γ^νK(γr). The direct correlation function c? (r, γ) is also considered and it is shown that for $\text{S}\text{≠ 0}$, $\text{lim}{}_{\mathrm{\gamma \to 0}}\text{γ}{}^{\mathrm{?\nu }}\text{c}\text{?}\text{(}\text{S}\text{γ}\text{, γ) = ?βK (}\text{S}\text{)}$, for all one-phase states, where β is the reciprocal temperature. Special cases of our results confirm those of other authors, including the well-known results of Ornstein and Zernike.