Relativistic Quantum Field Research Articles

Relativistic probability densities for location

Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions ψ( x , t) also for relativistic particles. Indeed, the Fourier transforms of normalized k -space amplitudes yield normalized functions ψ( x , t) which reproduce the standard k -space expectation values for energy and momentum from local momentum (pseudo-)densities ℘ μ ( x , t) = (ℏ/2i)[ψ +( x , t)∂ μ ψ( x , t) − ∂ μ ψ +( x , t) · ψ( x , t)]. However, in the case of bosonic fields, the wave packets ψ( x , t) are nonlocally related to the corresponding relativistic quantum fields ϕ( x , t), and therefore the canonical local energy-momentum densities and differ from ℘ μ ( x , t) and appear nonlocal in terms of the wave packets ψ( x , t). We examine the relation between the canonical energy density , the canonical charge density ϱ( x , t), the energy pseudo-density , and the Born density ∣ψ( x , t)∣2 for the massless free Klein–Gordon field. We find that those four proxies for particle location are tantalizingly close even in this extremely relativistic case: in spite of their nonlocal mathematical relations, they are mutually local in the sense that their maxima do not deviate beyond a common position uncertainty Δx. Indeed, they are practically indistinguishable in cases where we would expect a normalized quantum state to produce particle-like position signals, viz. if we are observing quanta with momenta p ≫ Δp ≥ ℏ/2Δx. We also translate our results to massless Dirac fields. Our results confirm and illustrate that the normalized energy density provides a suitable measure for positions of bosons, whereas normalized charge density ϱ( x , t)/q provides a suitable measure for fermions.

On the Resilience of Black Hole Evaporation: Gravitational Tunneling through Universal Horizons

Using a quantum tunneling derivation, we show the resilience of Hawking radiation in Lorentz violating gravity. In particular, we show that the standard derivation of the Hawking effect in relativistic quantum field theory can be extended to Lorentz breaking situations thanks to the presence of universal horizons (causal boundaries for infinite speed signals) inside black hole solutions. Correcting previous studies, we find that such boundaries are characterized by a universal temperature governed by their surface gravity. We also show that within the tunneling framework, given the pole structure and the tunneling path, only a vacuum state set in the preferred frame provides a consistent picture. Our results strongly suggest that the robustness of black hole thermodynamics is ultimately linked to the consistency of quantum field theories across causal boundaries.

Gravitationally induced entanglement in a harmonic trap

Recent work has shown that it may be possible to detect gravitationally induced entanglement in tabletop experiments in the not-too-distant future. However, there are at present no thoroughly developed models for this type of experiment where the entangled particles are treated more fundamentally as excitations of a relativistic quantum field, and with the measurements modeled using expectation values of field observables. Here we propose a thought experiment where two particles are initially prepared in a superposition of coherent states within a common three-dimensional (3D) harmonic trap. The particles then develop entanglement through their mutual gravitational interaction, which can be probed through particle position detection probabilities. The present work gives a nonrelativistic quantum mechanical analysis of the gravitationally induced entanglement of this system, which we term the ``gravitational harmonium'' due to its similarity to the harmonium model of approximate electron interactions in a helium atom; the entanglement is operationally determined through the matter wave interference visibility. The present work serves as the basis for a subsequent investigation, which models this system using quantum field theory, providing further insights into the quantum nature of gravitationally induced entanglement through relativistic corrections, together with an operational procedure to quantify the entanglement.

Entanglement generation and decoherence in a two-qubit system mediated by relativistic quantum field

Motivated by the Bose et al.-Matletto-Vedral (BMV) proposal for detecting quantum superposition of spacetime geometries, we study a toy model of a quantum entanglement generation between two spins (qubits) mediated by a relativistic free scalar field. After time evolution, spin correlation is generated through the interactions with the field. Because of the associated particle creation into an open system, the quantum state of spins is partially decohered. In this paper, we give a comprehensive study of the model based on the closed-time path formalism, focussing on relativistic causality and quantum mechanical complementarity. We calculate various quantities such as spin correlations, entanglement entropies, mutual information and negativity, and study their behaviors in various limiting situations. In particular, we calculate the mutual information of the two spins and compare it with spin correlation functions. We also discuss why no quantum entanglement can be generated unless both spins are causally affected by one another while spin correlations are generated.

Do We Have any Viable Solution to the Measurement Problem?

Wallace (2022) has recently argued that a number of popular approaches to the measurement problem can't be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only the unitary-only approaches to the measurement problem are viable. However, the unitary-only approaches face serious epistemic problems which may threaten their viability as solutions, and thus we consider that it remains an urgent outstanding problem to find a viable solution to the measurement problem which can be extended to relativistic quantum mechanics. In this article we seek to understand in general terms what such a thing might look like. We argue that in order to avoid serious epistemic problems, the solution must be a single-world realist approach, and we further argue that any single-world realist approach which is able to reproduce the predictions of relativistic quantum mechanics will most likely have the property that our observable reality does not supervene on dynamical, precisely-defined microscopic beables. Thus we suggest three possible routes for further exploration: observable reality could be approximate and emergent, as in relational quantum mechanics with the addition of cross-perspective links, or observable reality could supervene on beables which are not microscopically defined, as in the consistent histories approach, or observable reality could supervene on beables which are not dynamical, as in Kent's solution to the Lorentzian classical reality problem. We conclude that once all of these issues are taken into account, the options for a viable solution to the measurement problem are significantly narrowed down.

Significance of classically forbidden regions for short baseline neutrino experiments

Classically forbidden regions (CFRs) are common to both non-relativistic quantum mechanics, and to relativistic quantum field theory. It is known since 2001 that CFR contributes roughly sixteen percent of energy to the ground state of a simple harmonic oscillator (Adunas G. Z. et al., Gen. Relativ. Gravit., 33 (2001) 183). Similarly, quantum field theoretic arguments yield a non-zero amplitude for a massive particle to cross the light cone (that is, into the CFR). The signs of these amplitudes are opposite for fermions and antifermions. This has given rise to an erroneous conclusion that amplitude to cross the light cone is identically zero. This is true as long as a measurement does not reveal the considered object to be a particle or antiparticle. However, neutrino oscillation experiments do measure a neutrino ν, or an antineutrino . Here we show that in the context of neutrino oscillations these observations have the potential to resolve various short baseline anomalies for a sufficiently light lowest mass eigenstate. In addition, we make a concrete prediction for the upcoming results to be announced later this year by JSNS2.

The art of Schwinger and Feynman parametrizations

We present a derivation of the Schwinger parametrization and the Feynman parametrization in detail and their elementary applications. Although the parametrizations are essential to computing the loop integral arising in relativistic quantum field theory, their detailed derivations are not presented in usual textbooks. Beginning with an integral representation of the unity, we derive the Schwinger parametrization by performing multiple partial derivatives and utilizing the analyticity of the gamma function. The Feynman parametrization is derived by the partial-fraction decomposition and the change of variables introducing an additional delta function. Through the extensive employment of the analyticity of a complex function, we show the equivalence of those parametrizations. As applications of the parametrizations, we consider the combinatorial factor arising in the Feynman parametrization integral and the multivariate beta function. The combinatorial factor corresponds to an elementary integral embedded in the time-ordered product of the Dyson series in the time-dependent perturbation theory. We believe that the derivation presented here can be a good pedagogical example that students enhance their understanding of complex variables and train the use of the Dirac delta function in coordinate transformation.

Renormalization in a wavelet basis

Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based methods. We demonstrate the nonperturbative approach of regularization, renormalization, and the emergence of flowing coupling constant within the context of these methods. This is tested on a model of the particle in an attractive Dirac delta function potential in two spatial dimensions, which is known to demonstrate quintessential features found in a typical relativistic quantum field theory.

Decoherence: a numerical study

We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schrödinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states. We measure the speed with which decoherence spreads in the relativistic quantum field theory for a range of parameters. We find that it is less than the speed of light but faster than the speed of the massive charges in the initial state.

Geometric Event-Based Quantum Mechanics

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

The 𝒫(𝜑)₂ Model on de Sitter Space

In 1975 Figari, Høegh-Krohn and Nappi constructed theP(φ)2{\mathscr P}(\varphi )_2model on the de Sitter space. Here we complement their work with new results, which connect this model to various areas of mathematics. In particular, i.) we discuss the causal structure of de Sitter space and the induces representations of the Lorentz group. We show that the UIRs ofSO0(1,2)SO_0(1,2)for both the principal and the complementary series can be formulated on Hilbert spaces whose functions are supported on a Cauchy surface. We describe the free classical dynamical system in both its covariant and canonical form, and present the associated quantum one-particle KMS structures in the sense of Kay (1985). Furthermore, we discuss the localisation properties of one-particle wave functions and how these properties are inherited by the algebras of local observables.ii.) we describe the relations between the modular objects (in the sense of Tomita-Takesaki theory) associated to wedge algebras and the representations of the Lorentz group. We connect the representations of SO(1,2) to unitary representations ofSO(3)SO(3)on the Euclidean sphere, and discuss how theP(φ)2{\mathscr P}(\varphi )_2interaction can be represented by a rotation invariant vector in the Euclidean Fock space. We present a novel Osterwalder-Schrader reconstruction theorem, which shows that physicalinfrared problemsare absent on de Sitter space. As shown in Figari, Høegh-Krohn, and Nappi (1975), the ultraviolet problems are resolved just like on flat Minkowski space. We state the Haag–Kastler axioms for theP(φ)2{\mathscr P}(\varphi )_2model and we explain how thegeneratorsof the boosts and the rotations for the interacting quantum field theory arise from thestress-energy tensor. Finally, we show that the interacting quantum fields satisfy theequations of motionin their covariant form. In summary, we argue that the de SitterP(φ)2{\mathscr P}(\varphi )_2model is the simplest and most explicit relativistic quantum field theory, which satisfies basic expectations, like covariance, particle creation, stability and finite speed of propagation.

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.

Space-time-resolved quantum field approach to Klein-tunneling dynamics across a finite barrier

Klein tunneling takes place when a particle scatters on a supercritical barrier that is creating particle antiparticle pairs. The authors, using a space-time resolved relativistic quantum field theory approach, show that the transmitted particle does not tunnel through the barrier but is instead produced by modulations in the pair creation rate.

Solving hadron structures using the basis light-front quantization approach on quantum computers

Quantum computing has demonstrated the potential to revolutionize our understanding of nuclear, atomic, and molecular structure by obtaining forefront solutions in nonrelativistic quantum many-body theory. In this work, we show that quantum computing can be used to solve for the structure of hadrons, governed by strongly interacting relativistic quantum field theory. Following our previous work on light unflavored mesons as a relativistic bound-state problem within the nonperturbative Hamiltonian formalism, we present the numerical calculations on simulated quantum devices using the basis light-front quantization approach. We implement and compare the variational quantum eigensolver and the subspace-search variational quantum eigensolver to find the low-lying mass spectrum of the light meson system and its corresponding light-front wave functions as quantum states from ideal simulators, noisy simulators, and IBM quantum computers. Based on obtained quantum states, we evaluate the meson decay constants and parton distribution functions directly on the quantum circuits. Our calculations on the quantum computers and simulators are in reasonable agreement with accurate numerical solutions solved on classical computers when noises are moderately small, and our overall results are comparable with the available experimental data.

Quantum field simulator for dynamics in curved spacetime.

In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations1. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulatorof a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.

Complementarity and causal propagation of decoherence by measurement in relativistic quantum field theories

Entanglement generation by Newtonian gravitational potential between objects has been widely discussed to reveal the quantum nature of gravity. In this paper, we perform a quantum field theoretical analysis of a slightly modified version of the gedanken experiment by Mari and co-workers. We show that decoherence due to the presence of a detector propagates with the speed of light in terms of a retarded Green's function, as it should be consistent with causality of relativistic field theories. The quantum nature of fields, such as quantum fluctuations or emission of gravitons expressed in terms of the Keldysh Green's function also play important roles in the mechanism of decoherence due to on-shell particle creation. We also discuss the trade-off relation between the visibility of the interference and the distinguishability of the measurement, known as the wave particle duality, in our setup.

Boosting unstable particles

In relativity, there is no absolute notion of simultaneity, because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable particles. We show that, when a wavefunction is boosted, its tails travel one to the past and the other to the future. As a consequence, in the new frame of reference, the particle is in a quantum superposition "decayed + non decayed", where the property "decayed-ness" is entangled with the position. Since a particle cannot be localised in a region smaller than the Compton wavelength, there is a non-zero lower bound on this effect, which is fundamental in nature. The surprising implication is that, in a quantum world, decay probabilities can never be Lorentz-invariant. We show that this insight was the missing ingredient to reconcile the seemingly conflicting views about time dilation in relativistic quantum mechanics and quantum field theory.

Curved and expanding spacetime geometries in Bose-Einstein condensates

Phonons have the characteristic linear dispersion relation of massless relativistic particles. They arise as low energy excitations of Bose-Einstein condensates and, in nonhomogeneous situations, are governed by a space- and time-dependent acoustic metric. We discuss how this metric can be experimentally designed to realize curved spacetime geometries, in particular, expanding Friedmann-Lema\^itre-Robertson-Walker cosmologies, with negative, vanishing, or positive spatial curvature. A nonvanishing Hubble rate can be obtained through a time-dependent scattering length of the background condensate. For relativistic quantum fields this leads to the phenomenon of particle production, which we describe in detail. We explain how particle production and other interesting features of quantum field theory in curved spacetime can be tested in terms of experimentally accessible correlation functions.

Finite temperature description of an interacting Bose gas

We derive the equation of state of a Bose gas with contact interactions using relativistic quantum field theory. The calculation accounts for both thermal and quantum corrections up to one-loop order. We work in the Hartree-Fock-Bogoliubov approximation and follow Yukalov's prescription of introducing two chemical potentials, one for the condensed phase and another one for the excited phase, to circumvent the well-known Hohenberg-Martin dilemma. As a check on the formalism, we take the nonrelativistic limit and reproduce the known results. Finally, we translate our results to the hydrodynamical, two-fluid model for finite-temperature superfluids. Our results are relevant for the phenomenology of Bose-Einstein condensate and superfluid dark matter candidates, as well as the color-flavor locking phase of quark matter in neutron stars.

Divergence anomaly and Schwinger terms: Towards a consistent theory of anomalous classical fluids

In this Letter, anomaly, which is a generic feature of relativistic quantum field theory (QFT), is shown to be present in non-relativistic classical ideal fluid. Also, in this model we have found the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms in QFT. We work in the Hamiltonian framework, where Eulerian dynamical variables obey an anomalous algebra (with Schwinger terms) that is inherited from modified Poisson brackets, with Berry curvature corrections, among Lagrangian discrete coordinates. The divergence anomaly appears in the Hamiltonian equations of motion. A generalized form of the fluid velocity field can be identified by the ``anomalous velocity'' of Bloch band electrons appearing in the quantum Hall effect in condensed matter physics. Finally, we show that the divergence anomaly and Schwinger terms satisfy the well-known Adler consistency condition, and we mention possible scenarios that can be impacted by this new anomalous fluid theory.