Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum \phi^4_2

We perform a Monte Carlo simulation calculation of the critical coupling constant for the continuum {\lambda \over 4} \phi^4_2 theory. The critical coupling constant we obtain is [{\lambda \over \mu^2}]_crit=10.24(3).Comment: 11 pages, 4 figures, LaTe

Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example

We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected properties in the SG model. Some of them continue to have scale- invariant dynamics even in the presence of the non-conformal cosine interaction. For instance, it is shown that the Mandelstam operator for the bosonic representation of the Fermi field does {\it not} develop a mass term in the SG theory, contrary to what the real Fermi field in the massive Thirring model is expected to do. It is also shown that in the presence of the non-conformal interactions, some vertex operators have unique Lorentz spins, while others do not.Comment: 32 pages, Univ. of Illinois Preprint # ILL-(TH)-93-1

Introduction to quantum field theory

This book presents in a short volume the basics of quantum field theory and many body physics. The first part introduces the perturbative techniques without sophisticated apparatus and applies them to numerous problems including quantum electrodynamics (renormalization), Fermi and Bose gases, the Brueckner theory of nuclear system, liquid Helium and classical systems with noise. The material is clear, illustrative and the important points are stressed to help the reader get the understanding of what is crucial without overwhelming him with unnecessary detours or comments. The material in the

Renormalization in a classical lattice field theory

We formulate and describe a renormalization-group transformation for classical λφ4-field theory on a lattice. The main idea is to divide the angle variables of the oscillators into the fast ones (large momenta) and the slow ones (low momenta) and to average over the fast ones. This results in an effective Hamiltonian for the remaining slow modes, which can be compared with the starting Hamiltonian. We derive fixed-point conditions and obtain a scaling law for those classical solutions for which the renormalization step can be iterated. There is a striking resemblence between our classical treatment and the analogous procedure in quantum field theory, which we discuss in some detail

Renormalization in a classical lattice field theory

We formulate and describe a renormalization-group transformation for classical λφ4-field theory on a lattice. The main idea is to divide the angle variables of the oscillators into the fast ones (large momenta) and the slow ones (low momenta) and to average over the fast ones. This results in an effective Hamiltonian for the remaining slow modes, which can be compared with the starting Hamiltonian. We derive fixed-point conditions and obtain a scaling law for those classical solutions for which the renormalization step can be iterated. There is a striking resemblence between our classical treatment and the analogous procedure in quantum field theory, which we discuss in some detail

New non-local currents in the quantum sine-Gordon model

We obtain new conserved and Lorentz covariant non-local currents of the sine-Gordon system by treating this integrable, off-conformal system in the traditional canonical quantisation scheme. Our work and our currents are to be contrasted with those of Bernard and LeClair who employ Zamolodchikov's method, couched in the conformal perturbation theoretic framework, to obtain conserved currents [A.B. Zamolodchikov, Intern. J. Mod. Phys. A. 3 (1989) 743; A 4 (1989) 4235. D. Bernard and A LeClair, Commun. Math. Phys. 142 (1991) 99; Phys. Lett. 247 (1990) 309]

Long-range corrections to the Coulomb potential and their implications about weak interactions

We calculate corrections to the photon propagator due to the creation of virtual neutrino pairs. These are shown to result in long-range (1/r3- and 1/r5-type) corrections to the Coulomb potential. It is shown that these corrections are of significance because upper limits on their strengths lead to upper limits on the weak interaction cutoff λ, and on possible nonconservation of the "μ quantum number." A discussion is given of these upper limits as obtained from the present accuracy of Lamb-shift measurements

Remarks on the kinematics of multiperipheral processes

We study the implications of requiring that the "subenergies" si and the momentum transfers ti of a multiple production process be in the Regge domain. We show that even for very high-energy accelerator or cosmic-ray processes, the si are too small compared to the ti and the masses for one to apply a multi-Regge formalism for the two-particle → n-particle amplitude. Some alternatives are suggested