Hamiltonian Field Research Articles

Pion photoproduction of nucleon excited states with Hamiltonian effective field theory

We refine our previous calculation of multipole amplitude E0+ for pion photoproduction process, γN→πN. The treatment of final-state interactions is based upon an earlier analysis of pion-nucleon scattering within Hamiltonian effective field theory, supplemented by incorporating contributions from the N*(1650) and the KΛ coupled channel. The contribution from the bare state corresponding to the N*(1650) significantly enhances our results. Additionally, we also compute the multipole amplitude M1−, which is of direct relevance to the Roper resonance. The results are comparable with other dynamical coupled-channel models, even though the contribution from the bare state (interpreted as a 2s excitation) in this channel is small because of its large mass. Published by the American Physical Society 2024

On the Kostant-Souriau prequantization of scalar fields with polysymplectic structures

In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is based on using the natural geometric structures of polysymplectic Hamiltonian field theory to produce an analog of the Kostant-Souriau prequantization map familiar from geometric quantization. I show that while the resulting operators are quite different from those of canonical quantum field theory, the approach is nonetheless able to reproduce a few of canonical quantum field theory's most fundamental results. I finish by elaborating the current limitations of this approach and briefly discussing future prospects.

Coisotropic reduction in multisymplectic geometry

In this paper, we study coisotropic reduction in multisymplectic geometry. On the one hand, we give an interpretation of Hamiltonian multivector fields as Lagrangian submani- folds and prove that [Formula: see text]-coisotropic submanifolds induce a Lie subalgebra in the algebra of Hamiltonian [Formula: see text]-forms, similar to how coisotropic submanifolds in symplectic geometry induce a Lie subalgebra under the Poisson bracket. On the other hand, we extend the classical result of symplectic geometry of projection of Lagrangian submanifolds in coisotropic reduction to bundles of forms, which naturally carry a multisymplectic structure.

Canonical lifts in multisymplectic De Donder–Weyl Hamiltonian field theories

We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether’s theorem. The Klein–Gordon field, the Polyakov bosonic string, and Einstein–Cartan gravity in 3+1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint.

The geometry of the solution space of first order Hamiltonian field theories I: From particle dynamics to free electrodynamics

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems – as a (0+1)-dimensional field – and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.

A new canonical affine bracket formulation of Hamiltonian classical field theories of first order

It has been a long standing question how to extend, in the finite-dimensional setting, the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to this question by presenting a new completely canonical bracket formulation of Hamiltonian Classical Field Theories of first order on an arbitrary configuration bundle. It is obtained via the construction of the appropriate field-theoretic analogues of the Hamiltonian vector field and of the space of observables, via the introduction of a suitable canonical Lie algebra structure on the space of currents (the observables in field theories). This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. This is consistent with the fact that the space of currents and Hamiltonian sections are respectively, linear and affine. Our setting is illustrated with some examples including Continuum Mechanics and Yang–Mills theory.

Structure of the Λ(1670) resonance

We examine the internal structure of the Λ(1670) through an analysis of lattice QCD simulations and experimental data within Hamiltonian effective field theory. Two scenarios are presented. The first describes the Λ(1670) as a bare three-quark basis state, which mixes with the πΣ, K¯N, ηΛ and KΞ meson-baryon channels. In the second scenario, the Λ(1670) is dynamically generated from these isospin-0 coupled channels. The K−p scattering data and the pole structures of the Λ(1405) and the Λ(1670) can be simultaneously described well in both scenarios. However, a comparison of the finite-volume spectra to lattice QCD calculations reveals significant differences between these scenarios, with a clear preference for the first case. Thus the lattice QCD results play a crucial role in allowing us to distinguish between these two scenarios for the internal structure of the Λ(1670). Published by the American Physical Society 2024

Exceptional points unveiling quantum limit of fluorescence rates in non-Hermitian plexcitonic single-photon sources

Single-photon sources based on plexcitonic systems are notable for their fast fluorescence rates, typically >100 GHz. Our investigations reveal that exceptional points (EPs) may unveil the quantum limit of fluorescence rates in plexcitonic single-photon sources. By employing a non-Hermitian Hamiltonian framework and field quantization model, we demonstrate how the fluorescence rate can be ingeniously designed in an exemplified plexcitonic system consisting of a nanocube-on-mirror cavity and a single quantum emitter. We predict the highest fluorescence rates of 11.0, 13.9, and 14.7 THz at the EPs with typical dipole moments of 25, 30, and 35 D, respectively.

Study of the pion-mass dependence of ρ -meson properties in lattice QCD

We collect spectra extracted in the I=ℓ=1 ππ sector provided by various lattice QCD collaborations and study the mπ dependence of ρ-meson properties using Hamiltonian effective field theory (HEFT). In this unified analysis, the coupling constant and cutoff mass, characterizing the ρ−ππ vertex, are both found to be weakly dependent on mπ, while the mass of the bare ρ, associated with a simple quark-model state, shows a linear dependence on mπ2. Both the lattice results and experimental data can be described well. Drawing on HEFT’s ability to describe the pion mass dependence of resonances in a single formalism, we map the dependence of the phase shift as a function of mπ and expose interesting discrepancies in contemporary lattice QCD results. Published by the American Physical Society 2024

Euler–Poisson equations of a dancing spinning top, integrability and examples of analytical solutions

Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler–Poisson equations of a heavy body with fixed point, immersed in a fictitious gravity field. Using this analogy, we have found examples of analytical solutions for the case of a heavy symmetrical dancing top. They describe the motions with center of mass keeping its height fixed above the supporting plane. General solution to equations of a dancing top in terms of exponential of Hamiltonian field is given. An extra constraint, that take into account the reaction of supporting plane, leads to modification of the canonical Poisson structure and therefore the integrability according to Liouville is under the question.

Hypersensitivity and nephelauxetic effect of Er3+ in bismuth tellurite glass system

The optical absorption and emission properties of 20Li2O-xBi2O3-(78-x)TeO2-1Er2O3-1Ag glass system had been analyzed to investigate the hypersensitivity shift and its mechanism. According to the Covalent model, the hypersensitive shift indicated by the drop of F2 at x = 5 mol% can be attributed to charge transfer from O2– ligands to Er3+ ions meanwhile according to the Dielectric screening model, drop of F2 may due to Er3+ ions contraction. The dynamic coupling mechanism was used to explain hypersensitivity transition probabilities in non-centrosymmetric systems. The addition of Bi2O3 may modify the site symmetry of Er3+ ions and oxygen to a high asymmetry τ2, resulting in an asymmetrical electron distribution, thus increasing Er-O covalency, as shown by the maximum Ω2 value at x = 5 mol%. The Er3+ ions site symmetry was investigated using Hamiltonian crystal field fitting in the frame of the D4 point symmetry model, which yielded maximum crystal field strength Nv at x = 5 mol%, indicating low point symmetry distortion of the Er3+ ions site symmetry.

Conditions for symmetry reduction of polysymplectic and polycosymplectic structures

For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appeared in the literature, for a generalized version of the Marsden–Weinstein symmetry reduction theorem. Next, we prove a necessary and sufficient condition for polycosymplectic reduction. We relate polycosymplectic reduction in a one-to-one way to the reduction of an associated larger polysymplectic manifold. Throughout the paper, we provide examples and discuss special cases.

Delta Baryon Spectroscopy in Lattice QCD

A variational analysis is performed within the framework of lattice QCD to extract the masses of the spin-3/2 positive parity Delta ^+ baryons, including radial excitations. 2 + 1 flavour dynamical gauge-field configurations provided by the PACS-CS collaboration via the ILDG are considered. To improve our interpolator basis, we perform an iterative process of source and sink smearing and solve a generalised eigenvalue problem using the resulting fermion operators. We obtain a clear signal for the ground and first excited states at a light quark mass corresponding to m_pi = 413 MeV. Furthermore, we show that one can use the eigenvectors obtained in this method to investigate the nature of these states, allowing us to classify our results as 1s and 2s states for the ground and first excited states respectively. Finally, we briefly highlight the method of Hamiltonian effective field theory which can be used to make comparison with quark model expectations.

The study of P-wave Ds mesons in coupled channel framework

We developed a coupled channel framework connecting the quark model and lattice QCD to systematically investigate the inner structures of the four lowest P-wave Ds states. The cs¯ core and D(⁎)K channels were considered. The possible coupling of cs¯ with the D(⁎)K channel and the channel-channel potentials were described by the quark-pair creation model and the light meson exchanging model, respectively. The lattice QCD data was treated as input by using the hamiltonian effective field theory. Our results showed that the physical Ds0⁎(2317) and Ds1⁎(2460) contain important bare cs¯ core and D(⁎)K component, while the Ds1⁎(2536) and Ds2⁎(2573) are almost the cs¯ mesons.

The investigations of the P-wave Bs states combining quark model and lattice QCD in the coupled channel framework

Combining the quark model, the quark-pair-creation mechanism and B(*) overline{K} interaction, we have investigated the near-threshold P-wave Bs states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the Ds sector by fitting the lattice data. The masses of the bottom-strange partners of the {D}_{s0}^{ast }(2317) and {D}_{s1}^{ast }(2460) are predicted to be {M}_{B_{s0}^{ast }}={5730.2}_{-1.5}^{+2.4} MeV and {M}_{B_{s1}^{ast }}={5769.6}_{-1.6}^{+2.4} MeV, respectively, which are well consistent with the lattice QCD component. The two P-wave Bs states are the mixtures of the bare overline{b}s core and B(*) overline{K} component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the 0+ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the T-matrix of the Boverline{K} scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.

Bound on energy dependence of chaos

We conjecture a chaos energy bound, an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories. The conjecture states that the Lyapunov exponent $\ensuremath{\lambda}(E)$ grows no faster than linearly in the total energy $E$ in the high energy limit. In other words, the exponent $c$ in $\ensuremath{\lambda}(E)\ensuremath{\propto}{E}^{c}(E\ensuremath{\rightarrow}\ensuremath{\infty})$ satisfies $c\ensuremath{\le}1$. This chaos energy bound stems from thermodynamic consistency of out-of-time-order correlators and applies to any classical/quantum system with finite $N/\mathrm{large}$ $N$ ($N$ is the number of degrees of freedom) under plausible physical conditions on the Hamiltonians. To the best of our knowledge the chaos energy bound is satisfied by any classically chaotic Hamiltonian system known, and is consistent with the cerebrated chaos bound by Maldacena, Shenker, and Stanford, which is for quantum cases at large $N$. We provide arguments supporting the conjecture for generic classically chaotic billiards and multiparticle systems. The existence of the chaos energy bound may put a fundamental constraint on physical systems and the Universe.

Vibrational resonance analysis of linear molecules using resummation of divergent Rayleigh–Schrödinger perturbation theory series

The large order Rayleigh–Schrödinger perturbation theory (RSPT) was applied for calculating vibrational states of linear molecules. Two molecules (CO2 and C2H2) were used as test cases with using of isomorphic Watson Hamiltonian and quartic force fields. For CO2 the Sayvetz condition can remove all degeneracies for purely vibrational states and the non-degenerate perturbation theory can be applied. However, an existence of two degenerate modes in C2H2 requires using the upgraded degenerate version of RSPT that was employed in this context for the first time. The dominating divergent behavior of such series requires the resummation technique that mimics the multivalued nature of the underlying solutions, and the applied quartic Padé–Hermite approximants (QPHA) provided full solution of the problem. Moreover, some mathematical properties of QPHA proved to be an efficient tool for studying resonance effects through the Katz theorem that controls the singular points of the eigenvalues on the complex plane. In the case of C2H2, not only all earlier observed classical resonances were confirmed and quantified, but also subtle interpolyad resonances (K2/55,K3/4555), proposed recently by Herman (2011) were described as well. Following the analysis, we found several novel resonances, of which we proposed one independent interpolyad resonance K2/4444. The complete analysis of such critical points provided the full resonance picture of all studied molecules.

Cotangent bundle reduction and Routh reduction for polysymplectic manifolds

We discuss Lagrangian and Hamiltonian field theories that are invariant under a symmetry group. We apply the polysymplectic reduction theorem for both types of field equations and we investigate aspects of the corresponding reconstruction process. We identify the polysymplectic structures that lie at the basis of cotangent bundle reduction and Routh reduction in this setting and we relate them by means of the Routhian function and its associated Legendre transformation. Throughout the paper we provide examples that illustrate various aspects of the results.

Regularization in nonperturbative extensions of effective field theory

The process of renormalization in nonperturbative Hamiltonian effective field theory (HEFT) is examined in the $\mathrm{\ensuremath{\Delta}}$-resonance scattering channel. As an extension of effective field theory incorporating the L\"uscher formalism, HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD. HEFT also provides phenomenological insight into the basis-state composition of the finite-volume eigenstates via the state eigenvectors. The Hamiltonian matrix is made finite through the introduction of finite-range regularization. The extent to which the established features of this regularization scheme survive in HEFT is examined. In a single-channel $\ensuremath{\pi}N$ analysis, fits to experimental phase shifts withstand large variations in the regularization parameter $\mathrm{\ensuremath{\Lambda}}$, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the L\"uscher formalism ensures the eigenvalues are insensitive to $\mathrm{\ensuremath{\Lambda}}$ variation in the single-channel case, the eigenstate composition varies with $\mathrm{\ensuremath{\Lambda}}$; the admission of short-distance interactions diminishes single-particle contributions to the states. In the two-channel $\ensuremath{\pi}N$, $\ensuremath{\pi}\mathrm{\ensuremath{\Delta}}$ analysis, $\mathrm{\ensuremath{\Lambda}}$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $\mathrm{\ensuremath{\Lambda}}$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $\ensuremath{\pi}\mathrm{\ensuremath{\Delta}}$ scattering channel. Future high-quality lattice QCD results will be able to discriminate $\mathrm{\ensuremath{\Lambda}}$, describe the inelasticity, and constrain a description of the basis-state composition of the energy eigenstates. Finally, HEFT has the unique ability to describe the quark-mass dependence of the finite-volume eigenstates. The robust nature of this capability is presented and used to confront current state-of-the-art lattice QCD calculations.

Pion photoproduction off nucleon with Hamiltonian effective field theory

We analyze the $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ process in the negative parity channel with Hamiltonian effective field theory, which is successful in studying the nucleon resonances associated with the meson-nucleon scattering and lattice QCD simulations. We provide the scattering amplitude of pion photoproduction and extract the electric dipole amplitudes ${E}_{0+}$. The bare ${N}^{*}(1535)$ is important for improving the consistency between our results and the experimental data.