PCT theorem, Wightman axioms and conformal bootstrap

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

Three ways to solve critical ϕ4 theory on 4 − 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger–Dyson equation

In this paper, we solve the two-point function of the lowest dimensional scalar operator in the critical [Formula: see text] theory on [Formula: see text] dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the cross-cap bootstrap equation, and the third is to solve the Schwinger–Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage.

NONCRITICAL STRING LIOUVILLE THEORY AND GEOMETRIC BOOTSTRAP HYPOTHESIS

The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu–Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.

THE AFFINE TODA S-MATRICES vs PERTURBATION THEORY

We present perturbative calculations for the Affine Toda Field Theory (ATFT) S-matrices to the second order in the coupling constants for [Formula: see text] and [Formula: see text] in general, to the fourth order for [Formula: see text] theory as well as to the sixth order for [Formula: see text] theory. Conventional Feynman–Dyson calculation method and the dispersion approach are used to calculate the complete form of the perturbation amplitudes in contrast to the pole residues in previous papers. The results agree with those S-matrices obtained in the S-matrix approach, namely those based on analyticity, unitarity, crossing and bootstrap equation.

Statistical Concepts in Particle Physics

A review is given of the level density formula in hadron physics, which has reached a completely developed state on the basis of the bootstrap equation. It is shown how the approximate formula

‘Statistical Bootstrap’ Equation of State for Cold Ultra-Dense Matter

The statistical bootstrap theory of hadrons predicts a particle level density which increases with mass like ϱ(m) = cmaexp bm. The motivation for this level density is explored and then it is used to derive an equation of state for zero-temperature ultra-dense (> 1017 g cm−3) matter. The nature, uses, and limitations of the equation of state are discussed.