Relativistic Field Theory Model Research Articles

Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model

In the present work, a relativistic relation that connects the difference of interacting and noninteracting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is derived. We show that the difference of integrated finite volume correlation functions converges rapidly to its infinite volume limit as the size of the periodic box is increased. The fast convergence of our proposed formalism is illustrated by analytic solutions of a contact interaction model, the perturbation theory calculation, and also the Monte Carlo simulation of a complex ϕ4 lattice field theory model. Published by the American Physical Society 2024

Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory

We present an investigation of the Clauser-Horne-Shimony-Holt (CHSH) inequality within a relativistic quantum field theory model built up with a pair of free massive scalar fields $({\ensuremath{\varphi}}_{A},{\ensuremath{\varphi}}_{B})$ where, as is customary, the indices $(A,B)$ refer to Alice and Bob, respectively. A set of bounded Hermitian operators is introduced by making use of the Weyl operators. A CHSH-type correlator is constructed and evaluated in the Fock vacuum by means of canonical quantization. Although the observed violation of the CHSH inequality turns out to be rather small as compared to Tsirelson's bound of quantum mechanics, the model can be employed for the study of Bell's inequalities in the more physical case of gauge theories such as the Higgs models, for which local Becchi-Rouet-Stora-Tyutin (BRST) invariant operators describing both the massive gauge boson as well as the Higgs particle have been devised. These operators can be naturally exponentiated, leading to BRST invariant type of Weyl operators useful to analyze Bell's inequalities within an invariant BRST environment.

Modular zero modes and sewing the states of QFT

We point out an important difference between continuum relativistic quantum field theory (QFT) and lattice models with dramatic consequences for the theory of multi-partite entanglement. On a lattice given a collection of density matrices ρ(1), ρ(2), ⋯, ρ(n) there is no guarantee that there exists an n-partite pure state |Ω〉12⋯n that reduces to these marginals. The state |Ω〉12⋯n exists only if the eigenvalues of the density matrices ρ(i) satisfy certain polygon inequalities. We show that in QFT, as opposed to lattice systems, splitting the space into n non-overlapping regions any collection of local states ω(1), ω(2), ⋯ ω(n) come from the restriction of a global pure state. The reason is that rotating any local state ω(i) by unitary Ui localized in the ith region we come arbitrarily close to any other local state ψ(i). We construct explicit examples of such local unitaries using the cocycle.

The emergence of time

Classically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum fluctuations. The fundamental difference between the two frameworks is that classical physics is commutative (simultaneous observables) while quantum physics is intrinsically noncommutative (Heisenberg uncertainty relations). In this sense, we may say that time is generated by noncommutativity; if this statement is correct, we should be able to derive time out of a noncommutative space. We know that a von Neumann algebra is a noncommutative space. About 50 years ago the Tomita–Takesaki modular theory revealed an intrinsic evolution associated with any given (faithful, normal) state of a von Neumann algebra, so a noncommutative space is intrinsically dynamical. This evolution is characterised by the Kubo–Martin–Schwinger thermal equilibrium condition in quantum statistical mechanics (Haag, Hugenholtz, Winnink), thus modular time is related to temperature. Indeed, positivity of temperature fixes a quantum-thermodynamical arrow of time. We shall sketch some aspects of our recent work extending the modular evolution to a quantum operation (completely positive map) level and how this gives a mathematically rigorous understanding of entropy bounds in physics and information theory. A key point is the relation with Jones’ index of subfactors. In the last part, we outline further recent entropy computations in relativistic quantum field theory models by operator algebraic methods, that can be read also within classical information theory. The information contained in a classical wave packet is defined by the modular theory of standard subspaces and related to the quantum null energy inequality.

Study of instability of the Fourier split-step method for the massive Gross–Neveu model

Stability properties of the well-known Fourier split-step method used to simulate a soliton and similar solutions of the nonlinear Dirac equations, known as the Gross–Neveu model, are studied numerically and analytically. Three distinct types of numerical instability that can occur in this case, are revealed and explained. While one of these types can be viewed as being related to the numerical instability occurring in simulations of the nonlinear Schrödinger equation, the other two types have not been studied or identified before, to the best of our knowledge. These two types of instability are unconditional, i.e. occur for arbitrarily small values of the time step. They also persist in the continuum limit, i.e. for arbitrarily fine spatial discretization. Moreover, one of them persists in the limit of an infinitely large computational domain. It is further demonstrated that similar instabilities also occur for other numerical methods applied to the Gross–Neveu soliton, as well as to certain solitons of another relativistic field theory model, the massive Thirring.

Properties of massive rotating protoneutron stars with hyperons: structure and universality

In this work, we study the properties and structure of a massive and rapidly rotating protoneutron star (PNS) with hyperon content. We follow several stages of quasi-stationary evolution in an approximate way at four discrete steps. We use a density-dependent relativistic mean field theory model and calculate different quantities such as mass, equatorial radius, moment of inertia, and quadrupole moment to get different rotating configurations up to the mass-shedding limit. We study the effect of the appearance of Λ, the lightest of all hyperons, on each of the evolutionary stages of the PNS. We also check its sensitivity to the inclusion of ϕ vector meson as a mediator of Λ–Λ interaction in detail. Finally, we investigate the universal relations between moment of inertia and compactness in the context of a hot and young compact object.

Possible maximum mass of dark matter existing in compact stars based on the self-interacting fermionic model

The dark matter admixed neutron stars (DANSs) are studied using the two-fluid TOV equations separately, in which the normal matter (NM) and dark matter (DM) are simulated by the relativistic mean field theory and self-interacting fermionic model, respectively. A universal relationship [Formula: see text] is suggested, where [Formula: see text] is the maximum mass of DM existing in DANSs, [Formula: see text] is the particle mass of DM ranging from 5[Formula: see text]GeV to 1[Formula: see text]TeV, [Formula: see text] is the interaction mass scale with the value 300[Formula: see text]GeV (0.1[Formula: see text]GeV) for weak (strong) interaction DM model. This simple formula connects directly the microcosmic nature of DM particle with its macrocosmic mass existing in DANSs. Meanwhile, such a formula exhibits that the existence of NM has little effect on [Formula: see text]. It is found that the ratio of radius of DM in DANSs over [Formula: see text] is a constant with the value about 12[Formula: see text] (7[Formula: see text]) for weak (strong) interaction DM cases. According to the calculated results, only for the strong interaction DM cases with [Formula: see text] to [Formula: see text][Formula: see text]GeV and central energy density [Formula: see text][Formula: see text]MeV/fm3, DM has obvious effect on the mass of compact star. Compared with the energy density of DM in the Milky Way galaxy, [Formula: see text][Formula: see text]MeV/fm3, the existence of DM might hardly affect the mass of compact stars in the Milky Way galaxy.

Kelvin wave and knot dynamics on entangled vortices

In this paper, starting from Biot–Savart mechanics for entangled vortex-membranes, a new theory — knot physics — is developed to explore the underlying physics of quantum mechanics. Owning to the conservation conditions of the volume of knots on vortices in incompressible fluid, the shape of knots will never be changed and the corresponding Kelvin waves cannot evolve smoothly. Instead, the knot can only be split. The knot-pieces evolve following the equation of motion of Biot–Savart equation that becomes Schrödinger equation for probability waves of knots. The classical functions for Kelvin waves become wave-functions for knots. The effective theory of perturbative entangled vortex-membranes becomes a traditional model of relativistic quantum field theory — a massive Dirac model. As a result, this work would help researchers to understand the mystery in quantum mechanics.

Higgs mechanism in superconducting structures

It is shown that in equilibrium superconducting structures with s-wave pairing, the unique part of the phase of the complex ordering parameter 〈ψ↑ψ↓〉 transforms into the longitudinal component of the vector potential as in the Abelian Higgs model of relativistic field theory. This analysis is based on a microscopic Hamiltonian of the system in the presence of an external static magnetic field and infinitely small Cooper pair sources. Impurities and nonsuperconducting barriers are assumed to be present, and the quantum nature of the induced electromagnetic field is taken into account. Quantization of the latter is done under the condition A0 = 0 (A0 is the scalar potential) that the invariance with respect to time-independent gauge transformations is not broken. Exact relations determining the quasi-averages 〈ψ↑ψ↓〉 are established. These relations play a key role in the new derivation of the mean-field equations discussed in this article. A new physical treatment of the Josephson effect (without a “phase difference”) is proposed on the basis of these results and some of its consequences are discussed.

A phase-space noncommutative picture of nuclear matter

Noncommutative features are introduced into a relativistic quantum field theory model of nuclear matter, the quantum hadrodynamics-I nuclear model (QHD-I). It is shown that the nuclear matter equation of state (NMEoS) depends on the fundamental momentum scale, [Formula: see text], introduced by the phase-space noncommutativity (NC). Although it is found that NC geometry does not affect the nucleon fields up to [Formula: see text], it affects the energy density, the pressure and other derivable quantities of the NMEoS, such as the nucleon effective mass. Under the conditions of saturation of the symmetric NM under consideration, the estimated value for the noncommutative parameter is [Formula: see text].

Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) − f(Tr).

Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings

The doubly-connected polygonal geometry of planar graphene rings is found to bring forth topological configurations for accessing nontrivial relativistic quantum field (RQF) theory models that carry beyond the constant-mass Dirac-fermion theory. These include generation of sign-alternating masses, solitonic excitations, and charge fractionization. The work integrates a RQF Lagrangian formulation with numerical tight-binding Aharonov-Bohm electronic spectra and the generalized position-dependent-mass Dirac equation. In contrast to armchair graphene rings (aGRGs) with pure metallic arms, certain classes of aGRGs with semiconducting arms, as well as with mixed metallic-semiconducting ones, are shown to exhibit properties of one-dimensional nontrivial topological insulators. This further reveals an alternative direction for realizing a graphene-based nontrivial topological insulator through the manipulation of the honeycomb lattice geometry, without a spin-orbit contribution.

Non-perturbative λΦ4 in D = 1 + 1: an example of the constructive quantum field theory approach in a schematic way

During the '70, several relativistic quantum field theory models in $D=1+1$ and also in $D=2+1$ have been constructed in a non-perturbative way. That was done in the so-called {\it constructive quantum field theory} approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of $\lambda\Phi^4$ (with $m>0$) in $D=1+1$. Because of the absence of ultraviolet divergences in its perturbative version, this simple example -although does not capture all the difficulties in the constructive quantum field theory approach- allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.

Commutators of the four-current and sum rules in relativistic nuclear models

There is a long-standing problem on the linearly energy-weighted sum of the excitation strengths in the relativistic field theory and nuclear models: The sum value should be positively definite, while its naive calculation using the current commutator or the double commutator of the excitation operator with Dirac Hamiltonian yields the value to vanish. This paradoxical contradiction is solved in an analytic way.

Mimicking Interacting Relativistic Theories with Stationary Pulses of Light

One of the most well known relativistic field theory models is the Thirring model. Its realization can demonstrate the famous prediction for the renormalization of mass due to interactions. However, experimental verification of the latter requires complex accelerator experiments whereas analytical solutions of the model can be extremely cumbersome to obtain. In this work, following Feynman's original proposal, we propose an alternative quantum system as a simulator of the Thirring model dynamics. Here, the relativistic particles are mimicked, counterintuitively, by polarized photons in a quantum nonlinear medium. We show that the entire set of regimes of the Thirring model--bosonic or fermionic, and massless or massive--can be faithfully reproduced using coherent light trapping techniques. The correlation functions of the model can be extracted by simple probing of the coherence functions of the output light using standard optical techniques.

On the effective density dependence of vertex functionals in relativistic hadron field theory

The effective density-dependent mean-field model of relativistic hadron field theory is applied to calculate properties of symmetric and pure neutron nuclear matter. In order to examine the reliability and behaviour of high- and low-density model extrapolations outside the region of underlying theory, new functional forms of meson–nucleon vertex functionals are proposed. Different functional classes of density dependence are used to parameterize the Dirac–Brueckner–Hartree–Fock calculations to establish an effective approach. Various models are then compared, and implications on the equation of state of nuclear matter and compact stars are discussed. Our results show that the choice of the specific density dependence of couplings has significant effects on high-density calculations.

Gradient flows and instantons at a Lifshitz point

I provide a broad framework to embed gradient flow equations in non–relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen–Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Hořava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3–manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z = 3. Some general connections with the Onsager–Machlup theory of non-equilibrium processes are also briefly discussed in this context. Thus, theories of Lifshitz type in d + 1 dimensions can be used as off-shell toy models for dynamical vacuum selection of relativistic field theories in d dimensions.

Conducting polymers and relativistic field theories

We review the origins, successes, and limitations of the surprising but valuable connection between “conducting” π-conjugated polymers and relativistic field theory models.

Possibility of enlarged core structure of N=15 neutron-rich nuclei

The recently measured interaction cross section data for 22 N, 23 O, and 24 Fi n a 12 C target at relativistic energies have been analysed in a few body Glauber model approach. Conventional fixed core-plus-neutron model for halo nuclei is unable to explain the observed enhanced cross section for these nuclei by any selection of the neutron orbitals. Microscopic calculations like many-body Monte Carlo shell model, relativistic mean field theory and cluster model are also shown to fail in describing the large difference if interaction cross section between 22 Oa nd 23 O. A possibility of core enlargement is suggested in these nuclei.  2001 Elsevier Science B.V. All rights reserved.

Effects of new nonlinear couplings in relativistic effective field theory

We extend the relativistic mean field theory model of Sugahara and Toki by adding new couplings suggested by modern effective field theories. An improved set of parameters is developed with the goal to test the ability of the models based on effective field theory to describe the properties of finite nuclei and, at the same time, to be consistent with the trends of Dirac-Brueckner-Hartree-Fock calculations at densities away from the saturation region. We compare our calculations with other relativistic nuclear force parameters for various nuclear phenomena.