Quantum Field Theory Description Research Articles

Photon uncertainty solves the Einstein-Podolsky-Rosen paradox

Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical description of "physical reality" implied an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, EPR concluded that Quantum Mechanics had to be incomplete. However, its extensions involving additional "hidden variables", allowing for the recovery of determinism and locality, have been disproved experimentally (Bell's theorem). Here, I present an opposite solution of the paradox based on the greater indeterminism of the modern Quantum Field Theory (QFT) description of Particle Physics, that prevents the preparation of any state having a definite number of particles. The resulting uncertainty in photons radiation has interesting consequences in Quantum Information Theory (e.g. cryptography and teleportation). Moreover, since it allows for less elements of EPR physical reality than the old non-relativistic Quantum Mechanics, QFT satisfies the EPR condition of completeness without the need of hidden variables. The residual physical reality does never violate locality, thus the unique objective proof of "quantum nonlocality" is removed in an interpretation-independent way. On the other hand, the supposed nonlocality of the EPR correlations turns out to be a problem of the interpretation of the theory. If we do not rely on hidden variables or new physics beyond QFT, the unique viable interpretation is a minimal statistical one, that preserves locality and Lorentz symmetry.

An explicit construction of an Abelian topological quantum field theory in dimension [formula omitted

A geometrical description of an elementary topological quantum field theory based on the linking pairing is given, based on a talk given at the PIMS/Summer 1999 Workshop on invariants of 3-manifolds and topological quantum field theories at Nakoda Lodge, Alberta, Canada.

A worldsheet description of large Nc quantum field theory

The N c →∞ limit of a matrix quantum field theory is equivalent to summing only planar Feynman diagrams. The possibility of interpreting this sum as some kind worldsheet theory has been in the air ever since 't Hooft's original paper. We establish here just such a worldsheet description for a scalar quantum field with interaction term g Trφ 3/ N c , and we indicate how the approach might be extended to more general field theories.

The Generally Covariant Locality Principle – A New Paradigm for Local Quantum Field Theory

A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a "locally covariant quantum field theory". Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of *-algebras with unital injective *-endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual Haag-Kastler framework of nets of operator-algebras over a fixed spacetime background-manifold, together with covariant automorphic actions of the isometry-group of the background spacetime, can be re-gained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the time-slice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchy-evolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchy-evolution with respect to the spacetime metric is found to be a divergence-free quantity which has, as will be demonstrated in an example, the significance of an energy-momentum tensor for the locally covariant quantum field theory. Furthermore, we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness.

General physics motivations for numerical simulations of quantum field theory

In this introductory article a brief description of quantum field theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the regnant theory describing the interactions between quarks and gluons. I present an overview of what these calculations involve, why they are hard, and why they are tailor made for parallel computers. Finally, I try to communicate the excitement amongst the practitioners by giving examples of the quantities we will be able to calculate to within a few percent accuracy in the next five years.

Canted antiferromagnetic and spin-singlet quantum Hall states in double-layer systems

We present details of earlier studies [Zheng et al., Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al., 79, 917 (1997)] and additional results on double-layer quantum Hall systems at a total filling $\ensuremath{\nu}=2{\ensuremath{\nu}}_{1}$, where a single layer at filling ${\ensuremath{\nu}}_{1}$ forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case ${\ensuremath{\nu}}_{1}=1$, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well-separated layers, we find two double-layer quantum Hall phases: one with a finite interlayer antiferromagnetic spin ordering in the plane orthogonal to the applied field (the ``canted'' state), and the other a spin singlet. The quantum transitions between the various quantum Hall states are continuous, and are signaled by the softening of collective intersubband spin-density excitations. For the case of general ${\ensuremath{\nu}}_{1}$, closely related results are obtained by a semi-phenomenological continuum quantum field theory description of the low-lying spin excitations using a nonlinear $\ensuremath{\sigma}$ model. Because of its broken symmetry, the canted phase supports a linearly dispersing Goldstone mode and has a finite-temperature Kosterlitz-Thouless transition. We present results on the form of the phase diagram, the magnitude of the canted order parameter, the collective excitation dispersions, the specific heat, the form of the dynamic light-scattering spectrum at finite temperature, and the Kosterlitz-Thouless critical temperature. Our findings are consistent with recent experimental results.

Central functions and their physical implications

I define central functions c(g) and c'(g) in quantum field theory, useful to study the flow of the numbers of vector, spinor and scalar degrees of freedom from the UV limit to the IR limit and basic ingredients for a description of quantum field theory as an interpolating theory between pairs of 4D conformal field theories. The key importance of the correlator of four stress-energy tensors is outlined in this respect. Then I focus the analysis on the behaviours of the central functions in QCD, computing their slopes in the UV critical point. To two-loops, c(g) and c'(g) point towards the expected IR directions. As a possible physical application, I argue that a closer study of the central functions might allow us to lower the upper bound on the number of generations to the observed value. Candidate all-order expressions for the central functions are compared with the predictions of electric-magnetic duality.

Mapping class groups for D = 2 + 1 quantum gravity and topological quantum field theories

A series of disjunctional techniques combining Cerf's original work on diffeomorphism extensions and the Smale-Hatcher Conjecture are used to determine the mapping class groups or homeotopy groups of three-manifolds in which Chern-Simons-Witten and 3-dimensional quantum gravity theories live. Four cases of interest are being considered, two of which focus on three-manifolds with topology M = Z g X R (g ⩾ 2) . We show that when the 3-manifold M g is endowed with only one boundary component, its mapping class group is trivial; whereas the mapping class group is non-zero when M g has two boundary components. As for proper 3-manifolds such as handlebody H g ( g ⩾ 2), we prove that the mapping class group is trivial when H g possesses one boundary component. In contrast, when endowed with no boundary component at all, H g has a highly non-trivial mapping class group. The original impetus for the present work draws on recent developments in 3-dimensional physics, most notably on Chern-Simons-Witten theories and their quantum gravity incarnations. In these theories, mapping class groups have been at the forefront of determining suitable quantizations, solving operator ordering problems, finding a suitable set of diffeomorphism-invariant observables, and detecting and cancelling global gravitational anomalies. The problem of finding a suitable set of mapping class group induced observables is singled out. In particular, we provide a generalization of the Nelson-Regge construction of diffeomorphism-invariant observables for 2 + 1 quantum gravity by showing that the set of mapping class group induced observables corresponds to the centralizer of non-trivial mapping class groups. For proper 3-handlebodies with non-trivial homeotopy groups, it is argued that the lack of a global time direction is a significant obstacle in the physical description of topological quantum field theories, including their quantum gravity incarnation. Because of the triviality of some 3-homeotopy groups, the message derived from the present work is that there are a limited number of 3-manifolds (proper or otherwise) in which one can define consistent theories of quantum gravity and/or Chern-Simons-Witten theories.

Quantum field-theory description of tunneling in the integer quantum Hall effect

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field-theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field-theory approach is well supported by a numerical diagonalization of the microscopic hamiltonian.

Polymers inO(N) symmetric quantum field theory in the double-scaling limit

Filamentary-surfaces randomly branched polymers can be represented byO(N) symmetric quantum field theories in the limit whereN→∞ and the coupling constantg→g c in a correlated manner. The statistical systems of randomly branched polymers are realized as dual diagrams of the Feynman graphs of the underlyingO(N) symmetric quantum field theory. The purpose of these studies is to gain intuition for the long-lasting search for a possible description of quantum field theory in terms of extended objects.

Quantum field theory for the multi-variable Alexander-Conway polynomial

We investigate in this paper the quantum field theory description of the multi-variable Alexander polynomial (Δ). We first study the WZW model on the GL(1, 1). It presents a number of interesting features including non-compactness, non-simplicity, 1/ k 2 quantum corrections, and logarithms in the current blocks. We compute the four-point functions, determine the scalar product of current blocks and make contact with the U q gl(1, 1) quantum group. We then discuss the gl(1,1) Chern-Simons model and recover the eight relations that uniquely determine Δ, as shown recently by Murakami. We discuss also how Δ can be computed by link surgery. The analysis runs into some difficulties due to the facts that Δ is zero in the braid group approach unless a strand is open, and that Δ vanishes for a split link. We propose some formal solutions to these. In appendices we give the full set of U q gl(1, 1) 6 j coefficients, we deal with details of the free field representations of gl(1, 1) (1), and we explain how the Burau matrix can be computed via monodromy and contour representation of a link, establishing the connection between quantum field theory and a recent paper by Moody.

Rediscovering the Newton-Wigner operator from a space-time description of quantum field theory

The Newton-Wigner position operator is rediscovered directly from a space-time description of quantum field theory which is based on the actual physical situation where particles travel between emitters and detectors. It avoids methods used in nonrelativistic quantum physics and so-called wave equations.

Unbounded GNS representations of a *-algebra in a Krein space

Given a *-algebra $$\mathfrak{A}$$ and a linear, nonpositive definite, functional on it, the GNS construction yields a representation of $$\mathfrak{A}$$ in an indefinite metric space. We show that, if the functional satisfies a suitable condition, expressed in terms of a conditional expectation on $$\mathfrak{A}$$ , then the representation space is a Krein space. This provides an abstract setup for the description of a massless quantum field theory.

Monte Carlo simulations for quantum field theories involving fermions

We present a new variant of a Monte Carlo procedure for euclidean quantum field theories with fermions. On a lattice every term contributing to the expansion of the fermion determinant is interpreted as a configuration of self-avoiding oriented closed loops which represent the fermionic vacuum fluctuations. These loops are related to Symanzik's polymer description of euclidean quantum field theory. The method is extended to the determination of fermionic Green's functions. We test our method on the Scalapino-Sugar model in one, two, three, and four dimensions. Good agreement with exactly known results is found.

On Virtual Representations of Symmetric Spaces and Their Analytic Continuation

In this paper we study a problem in group representation theory motivated by relativistic quantum field theory. One of the most powerful approaches to constructing models of relativistic quantum fields relies on Euclidean field theory, a description of quantum field theory in which time is purely imaginary. The basic objects of Euclidean field theory (the Euclidean Green's- or Schwinger functions) can often be expressed in terms of functional integrals. The construction of quantum field models is thereby reduced to quadratures. A well-known, simple example of this method is the reformulation of quantum mechanisms by means of Wiener integrals. (The fundamental solution of the Schrodinger equation, analytically continued to imaginary time, is given by the well-known Feynman-Kac formula; see e.g. [15], [19].) In this approach one faces the problem of analytic continuation back to real time. While this problem is elementary in non-relativistic quantum mechanics, it is rather intricate in relativistic quantum field theory. For some class of relativistic quantum field theories, a fairly general solution to this problem was given in papers by Osterwalder and

Microcanonical quantum gravity

Quantum gravity is equivalent to a statistical mechanical system of classical fields in 4 + 1 dimensions at temperatureħ. It is generically true that systems involving gravitation do not exist at fixed temperature. We therefore propose a fixed action description of quantum gravity. The formalism for a fixed action description of quantum field theory is developed. It is found to be equivalent to the canonical fixedħ formalism for renormalizable field theories. It is also found that, in precise analogy to the microcanonical formulation of statistical mechanics, it describes a wider class of theories than the canonical formalism.

Description of Non-Polynomial Quantum Field Theories by Superpropagator Method

The description of superpropagator method and its applications to the mesodynamics, weak interaction, electrodynamics involving gravity and the chiral invariant field theory is given. The low-energy behaviour of particles is described, taking into account the loop Feynman diagrams. The renormalizations of physical quantities are finite and are expressed in terms of coupling constants. Partly this work was reported at the Third International Conference on Non-Local Quantum Field Theory in 1973 at Alushta, USSR.