Sidney Coleman

Bio: Sidney Coleman is an academic researcher from Harvard University. The author has contributed to research in topics: Quantum field theory & Charge (physics). The author has an hindex of 48, co-authored 83 publications receiving 26177 citations. Previous affiliations of Sidney Coleman include Princeton University.

Radiative Corrections as the Origin of Spontaneous Symmetry Breaking

Abstract: We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. The scalar-to-vector mass ratio is computable as a power series in $e$, the electromagnetic coupling constant. We find, to lowest order, $\frac{{m}^{2}(S)}{{m}^{2}(V)}=(\frac{3}{2\ensuremath{\pi}})(\frac{{e}^{2}}{4\ensuremath{\pi}})$. We extend our analysis to non-Abelian gauge theories, and find qualitatively similar results. Our methods are also applicable to theories in which the tree approximation indicates the occurrence of spontaneous symmetry breakdown, but does not give complete information about its character. (This typically occurs when the scalar-meson part of the Lagrangian admits a greater symmetry group than the total Lagrangian.) We indicate how to use our methods in these cases.

Structure of phenomenological Lagrangians. 1.

Abstract: The general structure of phenomenological Lagrangian theories is investigated, and the possible transformation laws of the phenomenological fields under a group are discussed. The manifold spanned by the phenomenological fields has a special point, called the origin. Allowed changes in the field variables, which do not change the on-shell S matrix, must leave the origin fixed. By a suitable choice of fields, the transformations induced by the group on the manifold of the phenomenological fields can be made to have standard forms, which are described in detail. The mathematical problem is equivalent to that of finding all (nonlinear) realizations of a (compact, connected, semisimple) Lie group which become linear when restricted to a given subgroup. The relation between linear representations and nonlinear realization is discussed. The important special case of the chiral groups SU(2)×SU(2) and SU(3)×SU(3) is considered in detail.

Fate of the false vacuum: Semiclassical theory

Abstract: It is possible for a classical field theory to have two homogeneous stable equilibrium states with different energy densities. In the quantum version of the theory, the state of higher energy density becomes unstable through barrier penetration; it is a false vacuum. This is the first of two papers developing the qualitative and quantitative semiclassical theory of the decay of such a false vacuum for theories of a single scalar field with nonderivative interactions. In the limit of vanishing energy density between the two ground states, it is possible to obtain explicit expressions for the relevant quantities to leading order in $h$; in the more general case, the problem can be reduced to solving a single nonlinear ordinary differential equation.

The Fate of the False Vacuum. 1. Semiclassical Theory

Abstract: It is possible for a classical field theory to have two homogeneous stable equilibrium states with different energy densities. In the quantum version of the theory, the state of higher energy density becomes unstable through barrier penetration; it is a false vacuum. This is the first of two papers developing the qualitative and quantitative semiclassical theory of the decay of such a false vacuum for theories of a single scalar field with nonderivative interactions. In the limit of vanishing energy density between the two ground states, it is possible to obtain explicit expressions for the relevant quantities to leading order in h; in the more general case, the problem can be reduced to solving a single nonlinear ordinary differential equation.

Quantum sine-Gordon equation as the massive Thirring model

Abstract: The sine-Gordon equation is the theory of a massless scalar field in one space and one time dimension with interaction density proportional to $cos\ensuremath{\beta}\ensuremath{\phi}$, where $\ensuremath{\beta}$ is a real parameter. I show that if ${\ensuremath{\beta}}^{2}$ exceeds $8\ensuremath{\pi}$, the energy density of the theory is unbounded below; if ${\ensuremath{\beta}}^{2}$ equals $4\ensuremath{\pi}$, the theory is equivalent to the zero-charge sector of the theory of a free massive Fermi field; for other values of $\ensuremath{\beta}$, the theory is equivalent to the zero-charge sector of the massive Thirring model. The sine-Gordon soliton is identified with the fundamental fermion of the Thirring model.

Dynamics of dark energy

Abstract: We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Reaction-rate theory: fifty years after Kramers

Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Non-Abelian Anyons and Topological Quantum Computation

Abstract: Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{ u}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{ u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.