Relativistic Scalar Field Research Articles

Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory

The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter. Published by the American Physical Society 2024

A scalar field theory of 1+1-dimensional laser wakefield accelerators

Abstract A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed rectangular circularly-polarised laser pulse. An upper bound on the dimensionless amplitude a 0 of the laser pulse is determined as a function of the phase speed v of the wake. The asymptotic behaviour of the upper bound on a 0 as v → c is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on a 0 which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when v is sufficiently close to c.

Relativistic scalar fields canonical quantization in Einstein–Yang–Mills–Higgs’s rotating black hole space-time

The quantum theory of relativistic mechanics to deal with the scalar fields behavior in a curved space-time is represented by the Klein–Gordon equation. In this work, we will investigate the gravitationally bound states of massive and massless scalar fields around a Einstein–Yang–Mills–Higgs’s rotating black hole. After applying the standard separation of variables ansatz, we will show in detail how to obtain the novel exact solutions of the radial part of the governing Klein–Gordon equation and express the radial solution in terms of the Confluent Heun functions. By applying the bound state boundary conditions, the Confluent Heun functions are reduced to be polynomials that lead to energy quantization. We find that the scalar fields have complex-valued energy levels that indicate the decaying/growing bound states known as quasibound states. In the end, using the exact radial solution, we derive the radiation distribution function of the black hole’s outer horizon to obtain the equation of the Hawking temperature.

A Study of Spin 1 Unruh–De Witt Detectors

A study of the interaction of spin 1 Unruh–De Witt detectors with a relativistic scalar quantum field is presented here. After tracing out the field modes, the resulting density matrix for a bipartite qutrit system is employed to investigate the violation of the Bell–CHSH inequality. Unlike the case of spin 1/2, for which the effects of the quantum field result in a decrease in the size of violation, in the case of spin 1, both a decrease or an increase in the size of the violation may occur. This effect is ascribed to the fact that Tsirelson’s bound is not saturated in the case of qutrits.

Dynamics of Carrollian scalar fields

Abstract Adopting an intrinsic Carrollian viewpoint, we show that the generic Carrollian scalar field action is a combination of electric and magnetic actions, found in the literature by taking the Carrollian limit of the relativistic scalar field. This leads to non-trivial dynamics: even a single particle with non-vanishing energy can move in Carrollian physics.

Scalar fields, localized structures and the Starobinsky model

This work deals with the presence of localized static structures in the real line, described by relativistic real scalar fields in two spacetime dimensions. We consider models featuring both standard and modified kinematics, where we employ two intriguing potentials supporting defect solutions. The first potential can transform kink into compacton in the standard framework, while the second one is based on the inflationary Starobinsky model. Interesting possibilities unseen in previous investigations are described, in particular, for the case related to the Starobinsky potential. The addressed potentials are inserted into a broader framework, and so the extended models are described by a wider set of solutions. This investigation also reveals the presence of the twinlike behaviour for a specific compact configuration, which solves two distinct models.

Relativistic massive and massless scalar fields bound to the Bumblebee gravity's black hole

In this letter, we examine massive and massless scalar quasibound states bound in the static spherically symmetric black hole solution of the Einstein-Bumblebee space-time. We start with constructing the governing relativistic fields' dynamical equation, i.e. the Klein-Gordon equation, component by component. With the help of the ansatz of separation of variables, we find the exact solution of the angular part in terms of Spherical Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that reveals a complex-valued energy levels expression for the case of massive scalar, where the real part is the scalar particle's energy and the imaginary part represents the quasibound state's decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe decaying relativistic states bound in the black hole's gravitational potential well. At the end, we investigate the Hawking radiation of the static Bumblebee black hole's horizon by deriving and investigating the radiation distribution function.

The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation

In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.

Continuum Limit of the Green Function in Scaled Affine φ44 Quantum Euclidean Covariant Relativistic Field Theory

Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the φ44-scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- and two-point functions. Affine quantization leads to a completely satisfactory quantization of field theories in situations involving scaled behavior, leading to an unexpected term, ℏ2/φ2, which arises only in the quantum aspects.

Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field

Using the relativistic complex scalar field model with a repulsive self-interaction, we discuss the ground state structure of charged pion condensation under the coexistence of parallel rotation and magnetic field. Our previous study found that the density distribution profile of the condensates is a supergiant quantum vortex phase and change with rotational speed and coupling constant. In this work, we further discover vortex lattice structures in the condensates under conditions of small rotation and strong coupling constant. This mechanism can be thought of as electrical superconductivity: Vortex lattices are created to better adapt to changes in rotation and interaction. Furthermore, large rotation and weak coupling constant are more likely to cause the vortex lattices to be destroyed and form a giant quantum vortex similar to a doughnut. We expect this phenomenon can be observed in the relativistic noncentral heavy ion collisions with large rotation and strong magnetic field. Published by the American Physical Society 2024

Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis

We study nonequilibrium dynamics of relativistic N-component scalar field theories in Minkowski space-time in a classical statistical regime, where typical occupation numbers of modes are much larger than unity. In this strongly correlated system far from equilibrium, the role of different phenomena such as nonlinear wave propagation and defect dynamics remains to be clarified. We employ persistent homology to infer topological features of the nonequilibrium many-body system for different numbers of field components N via a hierarchy of cubical complexes. Specifically, we show that the persistent homology of local energy density fluctuations can give rise to signatures of self-similar scaling associated with topological defects, distinct from the scaling behavior of nonlinear wave modes. This contributes to the systematic understanding of the role of topological defects for far-from-equilibrium time evolutions of nonlinear many-body systems. Published by the American Physical Society 2024

Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole

In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.

Exact scalar quasibound states solutions of f(R) theory's static spherically symmetric black hole

Following the recent developments in black holes' quasibound states exact solutions by Senjaya (2023b,c), in this letter, we present a novel exact solution of quasibound states of a scalar around a static spherically symmetric black hole solution of f(R) theory of gravity. We start with the relativistic scalar field wave equation, i.e. the Klein-Gordon equation, isolating the radial equation and finally successfully obtain the exact radial wave solutions in terms of General Heun functions. Having the exact solutions in hand, the energy levels expression is obtained from the radial wave polynomial conditions. In the last part of this letter, the Hawking radiation is investigated via the Damour-Ruffini method and the Hawking temperature is obtained from radiation distribution function.

Quantum Scalar Field Theory Based on an Extended Least Action Principle

Recently it is shown that the non-relativistic quantum formulations can be derived from an extended least action principle Yang (2023). In this paper, we apply the principle to massive scalar fields, and derive the Schrödinger equation of the wave functional for the scalar fields. The principle extends the least action principle in classical field theory by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a field needs to exhibit in order to be observable. Second, there are constant random field fluctuations. A novel method is introduced to define the information metrics to measure additional observable information due to the field fluctuations, which is then converted to the additional action through the first assumption. Applying the variation principle to minimize the total actions allows us to elegantly derive the transition probability of field fluctuations, the uncertainty relation, and the Schrödinger equation of the wave functional. Furthermore, by defining the information metrics for field fluctuations using general definitions of relative entropy, we obtain a generalized Schrödinger equation of the wave functional that depends on the order of relative entropy. Our results demonstrate that the extended least action principle can be applied to derive both non-relativistic quantum mechanics and relativistic quantum scalar field theory. We expect it can be further used to obtain quantum theory for non-scalar fields.

Real-time dynamics of false vacuum decay

We investigate false vacuum decay of a relativistic scalar field initialized in the metastable minimum of an asymmetric double-well potential. The transition to the true ground state is a well-defined initial-value problem in real time, which can be formulated in nonequilibrium quantum field theory on a closed time path. We employ the nonperturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion. We also compare to classical-statistical field theory simulations on a lattice in the high-temperature regime. By this, we demonstrate that the real-time decay rates are comparable to those obtained from the conventional Euclidean (bounce) approach. In general, we find that the decay rates are time dependent. For a more comprehensive description of the dynamics, we extract a time-dependent effective potential, which becomes convex during the nonequilibrium transition process. By solving the quantum evolution equations for the one- and two-point correlation functions for vacuum initial conditions, we demonstrate that quantum corrections can lead to transitions that are not captured by classical-statistical approximations. Published by the American Physical Society 2024

Impurity-doped scalar fields in arbitrary dimensions

We investigate the presence of localized structures for relativistic scalar fields coupled to impurities in arbitrary spatial dimensions. Such systems present spatial inhomogeneity, realized through the inclusion of explicit coordinate dependence in the Lagrangian. It is shown that, in stark contrast to the impurity-free scenario, Derrick's argument does not present a strong hindrance to the existence of stable solutions in this case. Bogomol'nyi equations giving rise to global minima of the energy are found, and some of the ensuing BPS configurations are presented.

Remarks on the Bell-Clauser-Horne-Shimony-Holt inequality

We discuss the relationship between the Bogoliubov transformations, squeezed states, entanglement, and maximum violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. In particular, we point out that the construction of the four bounded operators entering the Bell-CHSH inequality can be worked out in a simple and general way, covering a large variety of models, ranging from quantum mechanism to relativistic quantum field theories. Various examples are employed to illustrate the above mentioned framework. We start by considering a pair of entangled spin-one particles and a squeezed oscillator in quantum mechanics, moving then to the relativistic complex quantum scalar field and to the analysis of the vacuum state in Minkowski space-time in terms of the left and right Rindler modes. In the latter case, the Bell-CHSH inequality turns out to be parametrized by the Unruh temperature.

Non-linear effective field theory simulators in two-fluid interfaces

Analogue gravity offers an approach for testing the universality and robustness of quantum field theories in curved spacetimes and validating them using down-to-earth, laboratory-based experiments. Fluid interfaces are a promising framework for creating these gravity simulators and have successfully replicated phenomena such as Hawking radiation and black hole superradiance. Recent work has shown that hydrodynamical instabilities on the interface between two fluids can capture features of the post-inflationary thermalisation of the Early Universe. In this study, we extend fluid dynamics methods to develop an effective field theory for the interface between two fluids, demonstrating the equivalence between the governing equations and a relativistic scalar field in an analogue spacetime. We also show that the interfacial height field serves as the analogue relativistic field even in a nonlinear, interacting field theory. We propose that these mathematical equivalences can be extrapolated to probe regimes where calculations are challenging or impractical. Our work provides a new framework for simulating far-from-equilibrium cosmological and gravitational scenarios in the laboratory.

Conserved currents from nonlocal constants in relativistic scalar field theories

Conserved currents from nonlocal constants in relativistic scalar field theories

Weak Neutrino (Antineutrino) Charged-Current Responses and Scaling for Nuclear Matter in the Relativistic Mean Field

A systematic analysis of the weak responses for charged-current quasielastic neutrino-nucleus reactions is presented within the scheme of a fully relativistic microscopic model considering momentum-dependent scalar and vector mean field potentials in both the initial and final nucleon states. The responses obtained are compared with the ones corresponding to simpler approaches: energy-independent potentials and the relativistic plane wave limit in the final state, i.e., no potentials applied to the outgoing particle. The analysis is also extended to the scaling phenomenon, which provides additional information regarding nuclear dynamics. Results for the scaling function are shown for various nuclei and different values of the transferred momentum in order to analyze the behavior of the relativistic scalar and vector mean field potentials.