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Gerald V. Dunne

Publications and source records attributed to Gerald V. Dunne.

At least 73 records · Page 4Linked to original sources
arXiv2014

Super-Adiabatic Particle Number in Schwinger and de Sitter Particle Production

We consider the time evolution of the adiabatic particle number in both time-dependent electric fields and in de Sitter spaces, and define a super-adiabatic particle number in which the (divergent) adiabatic expansion is truncated at optimal order. In this super-adiabatic basis, the particle number evolves smoothly in time, according to Berry's universal adiabatic smoothing of the Stokes phenomenon. This super-adiabatic basis also illustrates clearly the quantum interference effects associated with particle production, in particular for sequences of time-dependent electric field pulses, and in eternal de Sitter space where there is constructive interference in even dimensions, and destructive interference in odd dimensions.

hep-th↗
arXiv2014

Generating Non-perturbative Physics from Perturbation Theory

In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from the perturbative expansion about the perturbative vacuum, combined with a single global boundary condition. This provides a dramatic realization of the principle of "resurgence", that the fluctuations about different semiclassical saddle points are related to one another in a precise quantitative manner. The analysis of quantum mechanics also generalizes to certain calculable regimes of quantum field theory.

hep-th↗
arXiv2014

Bernoulli Number Identities from Quantum Field Theory and Topological String Theory

We present a new method for the derivation of convolution identities for finite sums of products of Bernoulli numbers. Our approach is motivated by the role of these identities in quantum field theory and string theory. We first show that the Miki identity and the Faber-Pandharipande-Zagier (FPZ) identity are closely related, and give simple unified proofs which naturally yield a new Bernoulli number convolution identity. We then generalize each of these three identities into new families of convolution identities depending on a continuous parameter. We rederive a cubic generalization of Miki's identity due to Gessel and obtain a new similar identity generalizing the FPZ identity. The generalization of the method to the derivation of convolution identities of arbitrary order is outlined. We also describe an extension to identities which relate convolutions of Euler and Bernoulli numbers.

math.NT↗
arXiv2013

Full time-dependent Hartree-Fock solution of large N Gross-Neveu models

We find the general solution to the time-dependent Hartree-Fock problem for scattering solutions of the Gross-Neveu models, with both discrete (GN_2) and continuous (NJL_2) chiral symmetry. We find new multi-breather solutions both for the GN_2 model, generalizing the Dashen-Hasslacher-Neveu breather solution, and also new twisted breathers for the NJL_2 model. These solutions satisfy the full TDHF consistency conditions, and only in the special cases of GN_2 kink scattering do these conditions reduce to the integrable Sinh-Gordon equation. We also show that all baryons and breathers are composed of constituent twisted kinks of the NJL_2 model. Our solution depends crucially on a general class of transparent, time dependent Dirac potentials found recently by algebraic methods.

hep-th↗
arXiv2013

Transparent Dirac potentials in one dimension: the time-dependent case

We generalize the original derivation of transparent, static Schroedinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain all known transparent potentials as special cases and play a key role in the semi-classical solution of 1+1 dimensional, fermionic quantum field theories of Gross-Neveu and Nambu-Jona-Lasinio type.

hep-th↗
arXiv2013

Resurgence theory, ghost-instantons, and analytic continuation of path integrals

A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost--anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.

hep-th↗
arXiv2013

Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model

We explain the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, which unifies perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we find new non-perturbative `fracton' saddle point field configurations, and give a quantum interpretation of previously discovered `uniton' unstable classical solutions. The fractons lead to a semi-classical realization of IR renormalons in the circle-compactified theory, and yield the microscopic mechanism of the mass gap of the PCM.

hep-th↗
arXiv2013

Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model

We study non-self-dual classical solutions in the CP(N-1) model with Z_N twisted boundary conditions on the spatially compactified cylinder. These solutions have finite, and fractional, classical action and topological charge, and are `unstable' in the sense that the corresponding fluctuation operator has negative modes. We propose a physical interpretation of these solutions as saddle point configurations whose contributions to a resurgent semi-classical analysis of the quantum path integral are imaginary non-perturbative terms which must be cancelled by infrared renormalon terms generated in the perturbative sector.

hep-th↗
arXiv2012

Continuity and Resurgence: towards a continuum definition of the CP(N-1) model

We introduce a non-perturbative continuum framework to study the dynamics of quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's theory of resurgent trans-series, combined with the physical principle of continuity, in which spatial compactification and a Born-Oppenheimer approximation reduce QFT to quantum mechanics, while preventing all intervening rapid cross-overs or phase transitions. The reduced quantum mechanics contains the germ of all non-perturbative data, e.g., mass gap, of the QFT, all of which are calculable. For CP(N-1), the results obtained at arbitrary N are consistent with lattice and large-N results. These theories are perturbatively non-Borel summable and possess the elusive IR-renormalon singularities. The trans-series expansion, in which perturbative and non-perturbative effects are intertwined, encapsulates the multi-length-scale nature of the theory, and eliminates all perturbative and non-perturbative ambiguities under consistent analytic continuation of the coupling. We demonstrate the cancellation of the leading non-perturbative ambiguity in perturbation theory against the ambiguity in neutral bion amplitudes. This provides a weak-coupling interpretation of the IR-renormalon, and a theorem by Pham et al implies that the mass gap is a resurgent function, for which resummation of the semi-classical expansion yields finite exact results.

hep-th↗
arXiv2012

Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model

This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Ecalle resummation. The ideas from QFT use continuity on R^1 x S^1_L, i.e, the absence of any phase transition as N \to infinity, or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical configurations with actions 1/N (kink-instantons), 2/N (bions and bi-kinks), in units where the 2d instanton action is normalized to one. Perturbation theory possesses the IR-renormalon ambiguity that arises due to non-Borel summability of the large-orders perturbation series (of Gevrey-1 type), for which a microscopic cancellation mechanism was unknown. This divergence must be present because the corresponding expansion is on a singular Stokes ray in the complexified coupling constant plane, and the sum exhibits the Stokes phenomenon crossing the ray. We show that there is also a non-perturbative ambiguity inherent to certain neutral topological molecules (neutral bions and bion-anti-bions) in the semiclassical expansion. We find a set of "confluence equations" that encode the exact cancellation of the two different type of ambiguities. We show that a new notion of "graded resurgence triangle" is necessary to capture the path integral approach to resurgence, and that graded resurgence underlies a potentially rigorous definition of general QFTs. The mass gap and the Theta angle dependence of vacuum energy are calculated from first principles, and are in accord with large-N and lattice results.

hep-th↗
arXiv2012

The Chiral Magnetic Effect and Axial Anomalies

We give an elementary derivation of the chiral magnetic effect based on a strong magnetic field lowest-Landau-level projection in conjunction with the well-known axial anomalies in two- and four-dimensional space-time. The argument is general, based on a Schur decomposition of the Dirac operator. In the dimensionally reduced theory, the chiral magnetic effect is directly related to the relativistic form of the Peierls instability, leading to a spiral form of the condensate, the chiral magnetic spiral. We then discuss the competition between spin projection, due to a strong magnetic field, and chirality projection, due to an instanton, for light fermions in QCD and QED. The resulting asymmetric distortion of the zero modes and near-zero modes is another aspect of the chiral magnetic effect.

hep-th↗
arXiv2012

Heat Kernels and Zeta Functions on Fractals

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties.

math-ph↗
arXiv2012

The Heisenberg-Euler Effective Action: 75 years on

On this 75th anniversary of the publication of the Heisenberg-Euler paper on the full non-perturbative one-loop effective action for quantum electrodynamics I review their paper and discuss some of the impact it has had on quantum field theory.

hep-th↗
arXiv2011

Electric dipole moment induced by a QCD instanton in an external magnetic field

In the chiral magnetic effect, there is a competition between a strong magnetic field, which tends to project positively charged particles to have spin aligned along the magnetic field, and a chirality imbalance which may be produced locally by a topologically nontrivial gauge field such as an instanton. We study the properties of the Euclidean Dirac equation for a light fermion in the presence of both a constant abelian magnetic field and an SU(2) instanton. In particular, we analyze the zero modes analytically in various limits, both on R^4 and on the four-torus, in order to compare with recent lattice QCD results, and study the implications for the electric dipole moment.

hep-th↗
arXiv2011

Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production

We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair production rates, based on Feynman's worldline path integral formulation. Even though the path integral is a sum over all real closed trajectories in spacetime, the semiclassical description of non-perturbative pair production is dominated by closed classical trajectories that are generically complex. These closed trajectories contain segments associated with nonperturbative instanton suppression factors as well as segments producing phase factors that incorporate quantum interference effects. For a class of time-dependent electric fields we implement this procedure and demonstrate excellent quantitative agreement with alternative methods.

hep-th↗
arXiv2011

Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum

Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like $N^2$ for $N$ pulses [i.e., $N$ "slits"], and the functional form is well-described by a coherent multiple-slit expression. This behavior is generic for many driven quantum systems.

hep-th↗
arXiv2011

Baryon-baryon scattering in the Gross-Neveu model: the large N solution

The scattering of two Dashen-Hasslacher-Neveu (DHN) baryons in the large N Gross-Neveu model is solved exactly using the relativistic, time-dependent Hartree-Fock approach. Unlike the special case of kink-antikink scattering, the scattering of DHN baryons is sensitive to the back-reaction of the fermions bound inside the baryons. Correspondingly the solution is much more complicated than the kink-antikink scattering solutions, which can be expressed in terms of sinh-Gordon solitons. Nevertheless, we present a simple ansatz form that gives closed analytic expressions for both the space-time dependent mean fields and the Dirac spinors for all continuum and bound states. The solution can also be applied to the scattering of polarons and solitons in conducting polymers.

hep-th↗