Quantum Field Research Articles

Renormalization bi-Heyting algebra

Abstract We formulate a bi-Heyting algebra structure on the space of Feynman diagrams of a quantum field theory. This particular bi-Heyting algebra, which is originated from Feynman graphon representations of 1PI Green’s functions together with renormalization and core coproducts, provides some new topological treatments for the study of the asymptotics of 1PI Green’s functions and their corrections.

Fermionic entanglement in the presence of background electric and magnetic fields

In this study, we investigate the fermionic Schwinger effect in the presence of a constant magnetic field within (1+3)-dimensional Minkowski spacetime, considering both constant and pulsed electric fields. We analyze the correlations between Schwinger pairs for the vacuum and maximally entangled states of two fermionic fields. The correlations are quantified using entanglement entropy and Bell’s inequality violation for the vacuum state, while Bell’s inequality violation and mutual information are used for the maximally entangled state. One can observe the variation of the entanglement produced for fermionic modes with respect to different parameters. Additionally, we discuss the key differences from the behaviour of scalar fields in this context. This study offers deeper insights into quantum field theory and the dynamics of entanglement in the fermionic Schwinger effect.

Nonrenormalizable theories and finite formulation of QFT

In this paper, we show how the finite formulation of quantum field theory based on Callan-Symanzik equations can be generalized to the case of nonrenormalizable theories. We derive an equation for effective action for an arbitrary single scalar field theory, allowing us to perform computations without running in intermediate divergencies. We illustrate the method with the use of λϕ4+ϕ6/M2 theory by the explicit (and fully finite) calculations of the effective potential as well as two-, four- and six-point correlation functions at one-loop level and demonstrate that no quantum corrections to scalar mass m2, depending on M2 scale, are generated. Published by the American Physical Society 2025

Studying the 3d Ising surface CFTs on the fuzzy sphere

Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known as surface CFT in three dimensions, can be studied with the setup of fuzzy sphere. We consider the example of surface criticality of the 3d Ising CFT. We propose two schemes by cutting a boundary in the orbital space and the real space respectively to realise the ordinary and the normal surface CFTs on the fuzzy sphere. We obtain the operator spectra through state-operator correspondence. We observe integer spacing of the conformal multiplets, and thus provide direct evidence of conformal symmetry. We identify the ordinary surface primary oo, the displacement operator \mathrm{D}D and their conformal descendants and extract their scaling dimensions. We also study the one-point and two-point correlation functions and extract the bulk-to-surface OPE coefficients, some of which are reported for the first time. In addition, using the overlap of the bulk CFT state and the polarised state, we calculate the boundary central charges of the 3d Ising surface CFTs non-perturbatively. Other conformal data obtained in this way also agrees with prior methods. We also discuss future directions, such as special surface CFT, cone defects, and surfaces of other bulk CFTs.

Localization in quantum field theory for inertial and accelerated observers

Abstract We study the problem of localization in Quantum Field Theory (QFT) from the point of view of inertial and accelerated experimenters. We consider the Newton-Wigner, the Algebraic Quantum Field Theory (AQFT) and the modal localization schemes, which are, respectively, based on the orthogonality condition for states localized in disjoint regions of space, on the algebraic approach to QFT and on the representation of single particles as positive frequency solution of the field equation. We show that only the AQFT scheme obeys causality and physical invariance under diffeomorphisms.

Then, we consider the nonrelativistic limit of quantum fields in the Rindler frame. We demonstrate the convergence between the AQFT and the modal scheme and we show the emergence of the Born notion of localization of states and observables. Also, we study the scenario in which an experimenter prepares states over a background vacuum by means of nonrelativistic local operators and another experimenter carries out nonrelativistic local measurements in a different region. We find that the independence between preparation of states and measurements is not guaranteed when both experimenters are accelerated and the background state is different from Rindler vacuum, or when one of the two experimenters is inertial.

Quantum information and the C-theorem in de Sitter

Information-theoretic methods have led to significant advances in nonperturbative quantum field theory in flat space. In this work, we show that these ideas can be generalized to field theories in a fixed de Sitter space. Focusing on 1+1-dimensional field theories, we derive a boosted strong subadditivity inequality in de Sitter, and show that it implies a C-theorem for renormalization group flows. Additionally, using the relative entropy, we establish a Lorentzian bound on the entanglement and thermal entropies for a field theory inside the static patch. Finally, we discuss possible connections with recent developments using unitarity methods.

Isospectral local Hermitian theory for the PT -symmetric iϕ3 quantum field theory

We propose a new method to calculate perturbatively the isospectral Hermitian theory for the PT-symmetric iϕ3 quantum field theory in d dimensions, whose result is local. The result of the new method in 1 dimension reproduces our previous result in the ix3 quantum mechanics, and the new method can be seen as a generalization of our previous method to quantum field theory. We also find the isospectral local Hermitian theory has the same form in all dimensions and differs in coefficients only, and our previous results in quantum mechanics can be used directly to determine the form of the isospectral local Hermitian quantum field theory. Published by the American Physical Society 2025

Topological orders beyond topological quantum field theories

Systems displaying topological quantum order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interactions between anyons. As we illustrate, in some instances, . This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing exact dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping Landau-type theories to dual models with topological order, while preserving the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes. Published by the American Physical Society 2025

Flat space gravity at finite cutoff

Abstract We study the thermodynamics of Einstein gravity with vanishing cosmological constant subjected to conformal boundary conditions. Our focus is on comparing the series of subextensive terms to predictions from thermal effective field theory, with which we find agreement for the boundary theory on a spatial sphere, hyperbolic space, and flat space. We calculate the leading Wilson coefficients and observe that the first subextensive correction to the free energy is negative. This violates a conjectured bound on this coefficient in quantum field theory, which we interpret as a signal that gravity does not fully decouple in the putative boundary dual.

THE SYNERGIC ELECTROWEAK SYNCHROTRON RADIATION

The power spectral formula is derived for radiation of neutral electroweak bosons from an electron in a weak external homogeneous electromagnetic field. The calculation method is based on the source theory formulation of quantum field theory introduced by Schwinger. For ultra-relativistic electrons, it is derived that the Z0 emission rate is suppressed relative to photon emission. This implies that the decay of electron into W-boson and neutrino is also exponentially small under similar conditions. The article is written in the form of mathematical simplicity and the Schwinger pedagogical clarity.

Capturing Strong Correlation in Molecules with Phaseless Auxiliary-Field Quantum Monte Carlo Using Generalized Hartree-Fock Trial Wave Functions.

Generalized Hartree-Fock (GHF) is a long-established electronic structure method that can lower the energy (compared to spin-restricted variants) by breaking physical wave function symmetries, namely and . After an exposition of GHF theory, we assess the use of GHF trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC-G) calculations of strongly correlated molecular systems including symmetrically stretched hydrogen rings, carbon dioxide, and dioxygen. Imaginary time propagation is able to restore symmetry and yields energies of comparable or better accuracy than CCSD(T) with unrestricted HF and GHF references, and consistently smooth dissociation curves─a remarkable result given the relative scalability of ph-AFQMC-G to larger system sizes. The present exploration of model strongly correlated systems marks a promising starting point for future studies of more chemically relevant molecules, and demonstrates that ph-AFQMC-G provides a highly accurate (and, in contrast to active-space-based trials, relatively black box and always size-consistent) description of challenging systems exhibiting, e.g., antiferromagnetic coupling and/or geometric spin frustration.

A new approach in classical Klein-Gordon cosmology: “Small Bangs”, inflation and Dark Energy

Abstract In this work, we analyze the cosmological model in which the expansion is driven by a classical, free Klein-Gordon field on a flat, four-dimensional Friedmann-Lemaitre-Robertson-Walker spacetime. The model allows for arbitrary mass, non-zero cosmological constant and coupling to curvature. We find that there are strong restrictions to the parameter space, due to the requirement for the reality of the field values. At early cosmological times, we observe Big Bang singularities, solutions where the scale factor asymptotically approaches zero, and Small Bangs. The latter are solutions for which the Hubble parameter diverges at a finite value of the scale factor. They appear generically in our model for certain curvature couplings. An early inflationary era is observed for a specific value of the curvature coupling without further assumptions (unlike in many other inflationary models). A late-time Dark Energy period is present for all solutions with positive cosmological constant, numerically suggesting that a “cosmic no-hair” theorem holds under more general assumptions than the original Wald version which relies on classical energy conditions. The classical fields in consideration can be viewed as resembling one-point functions of a semiclassical model, in which the cosmological expansion is driven by a quantum field.

Exploring Absolute Retract in Regular Hayward Black Holes and Their Implications for Astrophysics

ABSTRACTIn this article, we study and describe the topology of the spherically symmetric and regular (with no singularity in its event horizon) black hole, which is called Hayward black hole. We use the symmetric metric for this object, associated with the Euler‐Lagrangian equation, to derive various types of geodesic equations and components of a subspace geodesic. Under certain conditions, this approach allows us to deduce three types of absolute retractions representing the particle's motion along different axes within a 3‐D subspace. These retractions could potentially describe the region of the event horizon of Hayward black holes. We show that the radial geodesics describe motion directly toward the black hole's center, while tangential geodesics illustrate paths without angular displacement. Spacetime curvature near the event horizon emphasizes the intense gravitational effects and distortions caused by the black hole's mass. Particle motion in subspace represents constrained tangential dynamics, providing insights into localized spacetime. In addition, the study of the Hayward black hole (topology and geometry) is valuable for our understanding of general relativity, exploring the quantum field of gravity implications, and contribute to the fields of mathematical physics and astrophysics.

Exploring novel solitary wave phenomena in Klein–Gordon equation using ϕ6 model expansion method

In this study, the ϕ6-model expansion method is showed to be useful for finding solitary wave solutions to the Klein–Gordon (KG) equation. We develop a variety of solutions, including Jacobi elliptic functions, hyperbolic forms, and trigonometric forms, so greatly enhancing the range of exact solutions attainable. The 2D, 3D, and contour plots clearly show different types of solitary waves, like bright, dark, singular, and periodic solitons. This gives us a lot of information about how the KG equation doesn’t work in a straight line. Our findings highlight the ϕ6 model as a powerful tool to study nonlinear wave equations, improve our understanding of their complex dynamics, and increase the scope for theoretical exploration. The ϕ6 model expansion technique is exceptionally adaptable and may be utilised for a wide array of nonlinear partial differential equations. Despite its versatility, the technique may not be applicable to all nonlinear PDEs, especially those that do not meet the specified requirements or structures manageable by this technique. In theoretical physics, particularly in field theory and quantum mechanics, the Klein–Gordon equation is a classical model. By studying this model, we can illustrate the waves and particles movements at relativistic speeds. Among other areas, its significance in cosmology, quantum field theory, and the study of nonlinear optics are widely considered. Additionally, it provides exact solutions and nonlinear dynamics have various applications in applied mathematics and physics. The study is novel because it provides a new understanding of the complex behaviours and various waveforms of the controlling model by means of detailed evaluation. Future research could focus on further exploring the stability and physical implications of these solutions under different conditions, thereby advancing our knowledge of nonlinear wave phenomena and their applications in physics and beyond.

Local description of decoherence of quantum superpositions by black holes and other bodies

It was previously shown that if an experimenter, Alice, puts a massive or charged body in a quantum spatial superposition, then the presence of a black hole (or more generally any Killing horizon) will eventually decohere the superposition. This decoherence was identified as resulting from the radiation of soft photons/gravitons through the horizon, thus suggesting that the global structure of the spacetime is essential for describing the decoherence. In this paper, we show that the decoherence can alternatively be described in terms of the local two-point function of the quantum field within Alice’s lab, without any direct reference to the horizon. From this point of view, the decoherence of Alice’s superposition in the presence of a black hole arises from the extremely low frequency Hawking quanta present in Alice’s lab. We explicitly calculate the decoherence occurring in Schwarzschild spacetime in the Unruh vacuum from the local viewpoint. We then use this viewpoint to elucidate (i) the differences in decoherence effects that would occur in Schwarzschild spacetime in the Boulware and Hartle-Hawking vacua; (ii) the difference in decoherence effects that would occur in Minkowski spacetime filled with a thermal bath as compared with Schwarzschild spacetime; (iii) the lack of decoherence in the spacetime of a static star even though the vacuum state outside the star is similar in many respects to the Boulware vacuum around a black hole; and (iv) the requirements on the degrees of freedom of a material body needed to produce a decoherence effect that mimics that of a black hole. Published by the American Physical Society 2025

Quantum integration of decay rates at second order in perturbation theory

Abstract We present the first quantum computation of a total decay rate in high-energy physics at second order in
perturbative quantum field theory. This work underscores the confluence of two recent cutting-edge advances.
On the one hand, the quantum integration algorithm Quantum Fourier Iterative Amplitude Estimation (QFIAE),
which efficiently decomposes the target function into its Fourier series through a quantum neural network before quantumly integrating the corresponding Fourier components. On the other hand, causal unitary in the
loop-tree duality (LTD), which exploits the causal properties of vacuum amplitudes in LTD to coherently generate all contributions with different numbers of final-state particles to a scattering or decay process, leading to
singularity-free integrands that are well suited for Fourier decomposition. We test the performance of the quantum algorithm with benchmark decay rates in a quantum simulator and in quantum hardware, and find accurate
theoretical predictions in both settings.

Generalized black hole entropy is von Neumann entropy

It has been argued that, while the individual terms in the generalized entropy, Sgen=A/4GN+Sext, are ill-defined in the semiclassical limit, their sum is well-defined if one takes into account perturbative quantum gravitational effects. The first term diverges as GN→0, and the second diverges due to the infinite entanglement across the horizon which is characteristic of type III von Neumann algebras. It was recently shown that the von Neumann algebra of observables “gravitationally dressed” to the mass of a Schwarzschild-AdS black hole or the energy of an observer in de Sitter spacetime admit a well-defined trace. The algebras are type II∞ (which does not admit a maximum entropy state) and type II1 (which admits a maximum entropy state) respectively, and the von Neumann entropy of “semiclassical” states was found to be (up to an additive constant) the generalized entropy. However, these arguments rely on the existence of a stationary “equilibrium (KMS) state” and do not apply to, for example, black holes formed from gravitational collapse, Kerr black holes, or black holes in asymptotically de Sitter spacetime. These spacetimes are stationary but not in thermal equilibrium. In this paper, we present a general framework for obtaining the algebra of “gravitationally dressed” observables for a linear, Klein-Gordon field on any spacetime with a (bifurcate) Killing horizon. We prove, assuming the existence of a stationary state—which is not necessarily KMS—and suitable asymptotic decay of solutions, a “structure theorem” that the algebra of “gravitationally dressed” observables always contains a type II factor of observables “localized” on the horizon. These assumptions have been rigorously proven in most cases of interest in this paper. Applying our general framework to the algebra of observables in the exterior of an asymptotically flat Kerr black hole where the fields are dressed to the black hole mass and angular momentum we find that the algebra is the product of a type II∞ algebra on the horizon and a type I∞ algebra at past null infinity. The full algebra is type II∞, and the von Neumann entropy of semiclassical states is the generalized entropy. In the case of Schwarzschild-de Sitter, despite the fact that we must introduce an observer, the algebra of observables dressed to the perturbed areas of the black hole and cosmological horizons is the product of type II∞ algebras on each horizon. The entropy of semiclassical states is given by the sum of the areas of the two horizons as well as the entropy of quantum fields in between the horizons. Our results suggest that in all cases where there exists another “boundary structure” (e.g., an asymptotic boundary or another Killing horizon) the algebra of observables is type II∞ and in the absence of such structures (e.g. de Sitter spacetime) the algebra is type II1. Published by the American Physical Society 2025

Introduction to Thermal Field Theory: From First Principles to Applications

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory.

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part Two)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part Two)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part One)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part One)