Quantum Field Research Articles

Making sense of ghosts

Ghosts have been a stumbling block in the development of a UV complete quantum field theory for gravity. We discuss how difficulties associated with ghosts are overcome in the context of 0+1d QFT. Obtaining a probability interpretation is the key issue, and for this we discuss how an appropriate inner product can be constructed to define a sensible Born rule. Ghost theories are intrinsically unitary and perturbatively stable. They can also display nonperburbative stability even when the corresponding normal theory does not. The spectra and propagators are numerically obtained at both weak and strong coupling. Normalizable wave functions are obtained for the energy eigenstates and they show a violation of normal parity. We discuss connections to PT-symmetric quantum mechanics.

Gluing together quantum field theory and quantum mechanics: A look at the Bell-Clauser-Horne-Shimony-Holt inequality

Gluing together quantum field theory and quantum mechanics: A look at the Bell-Clauser-Horne-Shimony-Holt inequality

Electron-positron pair creation under Gaussian and super-Gaussian pulse trains

The electron-positron pair (EPP) creation under Gaussian and super-Gaussian pulse trains are studied by the computational quantum field theory (CQFT) in the single-photon regime. The details of the EPP creation are studied from the time evolution of the EPP number, energy spectra and spatial distribution of the electrons. The results indicate that the final created EPPs is the non-linear accumulation of the multi-pulses, which depends on the time interval, pulse shape and pulse number. The optimal time interval can be chosen based on the pulse resonance condition, which is derived by the perturbation method. Besides, steeper super-Gaussian pulses and adding more pulses facilitate the EPP creation as well. The results indicate that, under optimal multi-pulse parameters, the number of the EPPs obtained is much larger than the sum of the EPPs created under the same number of single pulses. This finding not only can enhance the EPP creation, but also can improve the multi-pulse utilization and guide future experimental research on the EPP creation.

On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC

Abstract In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume $V_o$, known as the \emph{fiducial cell}. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of $V_o$ is in turn essential for assessing the minisuperspace description's validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous minisuperspaces within the canonical framework and apply it to a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory's canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogenenity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on $V_o$. We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different $V_o$, and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ``first reduced, then quantised" approach can be reproduced is identified and the conditions for this to be a good approximation are determined.

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light propagation in nonlinear optical fibers or photonic crystals where the refractive index has a q-deformed structure; and it also can be applied in studying shock waves, turbulence and rogue waves where the deformation introduces corrections to classical wave phenomena. Utilizing the (G′ωG′+G+r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\frac{{\\mathfrak {G}}^{\\prime }}{\\omega {\\mathfrak {G}}^{\\prime }+{\\mathfrak {G}}+r})$$\\end{document}-expansion technique, we derive novel analytical solutions that enhance our understanding of the underlying dynamics. Additionally, we employ a finite element method (extended cubic B-spline method) to validate our analytical findings and explore the behavior of the q-deformed equation under different parameter regimes. Our results demonstrate the versatility of the q-deformed framework in generating rich optical phenomena, paving the way for future research in both theoretical and applied physics.

The Accelerating Universe in a NoncommutativeAnalytically Continued Foliated Quantum Gravity

Abstract Based on an analytically continued Riemannian foliated quantum gravity
super-Hamiltonian, known as Branch Cut Quantum Gravity (BCQG) we propose
a novel approach to investigating the effects of noncommutative geometry on a
minisuperspace of variables, influencing the acceleration behavior of the universe’s
wave function and the cosmic scale factor. Noncommutativity is introduced through
a deformation of the conventional Poisson algebra, enhanced with a symplectic
metric. The resulting symplectic manifold provides a natural setting that enables
an isomorphism between canonically conjugate dual vector spaces, spanning the
BCQG cosmic scale factor and its complementary quantum counterpart. Using this
formulation, we describe the dynamic evolution of the universe’s wave function, the
cosmic scale factor, and its complementary quantum image. Our results strongly
suggest that the noncommutative algebra induces late-time accelerated growth of the
wave function, the universe’s scale factor, and its complementary quantum counterpart,
offering a new perspective on explaining the accelerating cosmic expansion rate and
the inflationary period. In contrast to the inflationary model, where inflation requires
a remarkably fine-tuned set of initial conditions in a patch of the universe, analytically
continued non-commutative foliated quantum gravity captures short and long scales,
driving the evolutionary dynamics of the universe through a reconfiguration of the
primordial cosmic content of matter and energy. This reconfiguration is encapsulated
into a quantum field potential, which leads to the generation of relic gravitational
waves, a topic for future investigation. Graphical representations and contour plots
indicate a characteristic torsion (or twist) deformation of spacetime geometry. This
result introduces new speculative elements regarding the reconfiguration of matter and
energy as a driver of spacetime torsion deformation, generating relic gravitational waves
and serving as an alternative topological mechanism for the universe’s acceleration.
However, these assumptions require further investigation.

Pseudospectra of quasinormal modes and holography

The holographic duality (also known as AdS/CFT correspondence or gauge/gravity duality) postulates that strongly coupled quantum field theories can be described in a dual way in asymptotically anti-de Sitter space. One of the cornerstones of this duality is the description of thermal states as black holes with asymptotically anti-de Sitter boundary conditions. This idea has led to valuable insights into fields such as transport theory and relativistic hydrodynamics. In this context, the quasinormal modes of such black holes play a decisive role, and therefore their stability properties are of utmost interest for the holographic duality. We review recent results using the method of pseudospectra.

Quantum field theory of electrons and nuclei

Abstract We develop a non-relativistic quantum field theory of electrons and nuclei with Coulomb interactions. We derive the exact equations of motion and write these equations in the form of Hedin's equations for all species of identical particles involved. Theory derived allows the computation of exact observables and provides a rigorous starting point to derive approximations in a systematic way.

Topological symmetry in quantum field theory

We introduce a definition and framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a calculus of topological defects which takes advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called “gauging” and “condensation defects”), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.

Quantum-coherence-assisted dynamical phase transition in the one-dimensional transverse-field Ising model

Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.

From Complex Dynamics to Foundational Physics (Part 1)

As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradigms of foundational physics. There are, however, growing suspicions that both paradigms fail to hold somewhere above the Standard Model (SM) scale and in the realm of primordial cosmology. Evidence collected on multiple fronts indicates that emergence and complexity are universal features of far-from-equilibrium systems with many degrees of freedom. In line with these findings, Part 1 of the report explores the complex dynamics of evolving dimensional fluctuations beyond the SM scale. Part 2 outlines the role of complex dynamics in the nonintegrable sector of particle physics, Dark Matter condensation and the gravitational regime of the early Universe.

Quantum Perception and Quantum Computation

Quantum theory has led to the development of quantum technology and also advances in quantum technology further enhance our understanding of quantum theory. Among these technologies, quantum computing holds special importance as it is based on the quantum states concept, known as qubits or qudits. To advance quantum computation, it is crucial to deepen our understanding of quantum field theory. In this letter, we define quantum understanding as the first step towards this goal. Transitioning from classical to quantum perception is essential, as maintaining a classical viewpoint introduces numerous challenges in building a quantum computer. However, adopting quantum thinking mitigates these difficulties. This letter will first introduce quantum perception by examining the process of classical understanding and how this new approach to thinking transforms our perspective of nature. We will discuss how this shift in thinking provides a better conceptual understanding of the realization of quantum technology and quantum computing.

Hydrogen energy levels from the anomalous energy-momentum QED trace

Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb shift one-loop diagrams. Our calculations provide an argument against inclusion of the anomalous trace contribution as a separate term in the decomposition of the QED quantum field Hamiltonian and serve as an illustration how the trace anomaly is realized in the bound state QED. Published by the American Physical Society 2024

Life: An emergent property that passively qualifies matter or a purposive agency that actively controls matter?

Despite its abundance, life continues to be a mind-boggling mystery. Physical entities are made of matter-energy, and thus they are ontologically objective. The properties that emerge on a physical entity and characterize it are ontologically subjective and thus nonphysical. Emergent properties routinely appear on physical entities during assembly out of nowhere and disappear during disassembly. We can engineer the manifestation of desired properties by manipulating matter, but we seem to have no control over agencies. Agencies are characterized by causal power and thus the capacity to cause changes. Ontologically, agencies have primacy and supremacy. Unlike properties, agencies go beyond passively qualifying matter: they actively control matter. Many agencies can be identified in nature, such as the familiar agency of physics, comprised of the laws and forces of physics and controls the physical entities, and the quantum field agency which converts quanta of energy concisely into particles with a distinctive set of properties. In this paper it is discussed, based on careful observations, plausibility, logical consistency, and reasoned arguments, that enigmatic life is best characterized as a purposive agency that actively subjugates and controls matter rather than an emergent property that passively qualifies matter.

Bell-CHSH inequality and unitary operators

Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The ensuing modifications affecting both classical and quantum bounds are elucidated. The relevance of a particular class of unitary operators whose expectation values are real is pointed out. For these operators, the classical and quantum bounds remain unaltered, being given, respectively, by 2 and 22. As examples, we discuss the explicit realization of phase space Bell-CHSH inequality violation and the Weyl unitary operators for a real scalar field in relativistic Quantum Field Theory.

Investigation of PCVSi− defect in 4H–SiC as a candidate for a qubit

Abstract Exploration of spin defects in semiconductors for possible qubits encourages the development of the quantum field. Silicon carbide (SiC) is a suitable platform to carry spin defects, due to its excellent electrical, mechanical and optical properties, together with its convenience for crystallographic growth and doping processes. In this study, a negatively charged phosphorus-vacancy (PCVSi −) defect, consisting of a silicon vacancy and nearby substitution of a phosphorus atom to a carbon atom in 4H–SiC, is investigated by first-principles calculations. This defect is demonstrated to possess a high spin (S = 1) with relatively low formation energy. Computed zero-phonon line energy and zero-field splitting parameters of this defect are close to those of neutral divacancy (VCVSi 0), negatively charged nitrogen-vacancy center (NCVSi −) and some other color centers, which indicate a similarity of both optical and spin properties among them. Moreover, the electron spin coherence time of this defect turns out to be 1.15–1.40 ms. Such a long coherence time provides the defect with reliability for quantum information processing. Our results show that the PCVSi − defect can be a promising candidate for a qubit.

Self-sustained optomechanical state destruction triggered by the Kerr nonlinearity

Cavity optomechanics implements a unique platform where moving objects can be probed by quantum fields, either laser light or microwave signals. With a pump tone driving at a frequency above the cavity resonance, self-sustained oscillations can be triggered at large injected powers. These limit-cycle dynamics are particularly rich, presenting hysteretic behaviors, broad comb signals, and especially large motion amplitudes. All of these features can be exploited for both fundamental quantum research and engineering. Here we present low-temperature microwave experiments performed on a high-Q cavity resonance capacitively coupled to the flexure of a beam resonator. We study the limit-cycle dynamics parameter space as a function of pump parameters (detuning, power). Unexpectedly, we find that in a region of this parameter space the microwave resonance is irremediably destroyed: Only a dramatic power reset can restore the dynamics to its original state. The phenomenon can be understood as an optical instability linked to the Kerr nonlinearity of the cavity. A theory supporting this claim is presented, reproducing almost quantitatively the measurement. This remarkable feature might be further optimized and represents a new resource for quantum microwave circuits. Published by the American Physical Society 2024

Fermionic Casimir energy in Horava–Lifshitz scenario

In this work, we investigate the violation of Lorentz symmetry through the Casimir effect, one of the most intriguing phenomena in modern physics. The Casimir effect, which represents a macroscopic quantum force between two neutral conducting surfaces, is widely regarded as a triumph of Quantum Field Theory. In this study, we present new results for the Casimir effect, focusing on the contribution of mass associated with fermionic quantum fields confined between two large parallel plates, in the context of Lorentz symmetry violation within the Horava–Lifshitz formalism. To calculate the Casimir energy and pressure, we impose a MIT bag boundary condition on the two plates, compatible with the higher-order derivative term in the modified Dirac equation. Our results reveal a strong influence of Lorentz violation on the Casimir effect. We observe that the Casimir energy is significantly affected, both in intensity and sign, potentially resulting in a repulsive or attractive force between the plates, depending on the critical exponent associated with the Horava–Lifshitz formalism.

Energy change and Landauer’s principle in the interaction between qubit and quantum field theory

We give a general description of the system evolution under the interaction between qubit and quantum field theory up to the second order perturbation, which is also referred to as the simplified model of light-matter interaction. The results are classified into rotating and counter-rotating wave terms, the former corresponding to stimulated absorption and emission, and the latter to Unruh and anti-Unruh effects. We obtain not only the reduced density matrix of the qubit, but also the backreaction obtained by quantum field theory as the environment. The result shows that the energy variation of the quantum field theory is related to trajectory and the initial state of the qubit, the expectation values of the linear and quadratic field operators, and the temporal order product operator. When the qubit is in accelerated motion, the conventional Unruh effect causes the vacuum state to possess a “temperature”, which raises some doubts about the validity of Landauer’s principle. We prove that Landauer’s principle still holds for any state of motion.

The Spin-Statistics Theorem for Topological Quantum Field Theories

The Spin-Statistics Theorem for Topological Quantum Field Theories