Quantum Field Theory Research Articles

Anomalous higher order Ward identities in tensorial group field theories without closure constraint

Abstract The Ward-Takahashi identities are considered as the generalization of the Noether currents available to quantum field theory and include quantum fluctuation effects. Usually, they take the form of relations between correlation functions, which ultimately correspond to the relation between coupling constants of the theory. For this reason, they play a central role in the construction of renormalized theory, providing strong relations between counter-terms. Since last years, they have been intensively considered in the construction of approximate solutions for nonperturbative renormalization group of tensorial group field theories. The construction of these identities is based on the formal invariance of the partition function under a unitary transformation, and Ward’s identities result from a first-order expansion around the identity. Due to the group structure of the transformation under consideration, it is expected that a first-order expansion is indeed sufficient. We show in this article that this does not seem to be the case for a complex tensor theory model, with a kinetic term involving a Laplacian.

Mourre Theory and Asymptotic Observables in Local Relativistic Quantum Field Theory

We prove the convergence of Araki–Haag detectors in any Haag–Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki–Haag detector on states of bounded energy, which are selected from the absolutely continuous part of the energy-momentum spectrum sufficiently close to the lower boundary of the multi-particle spectrum. These states essentially encompass those states in the multi-particle spectrum lying below the three-particle threshold. In our proof, we draw on insights from proofs of asymptotic completeness in quantum mechanics. Notably, we apply Mourre’s conjugate operator method for the first time within the framework of Haag–Kastler quantum field theory. Furthermore, we discuss applications of our findings for the problem of asymptotic completeness in local relativistic quantum field theory.

Two types of series expansions valid at strong coupling

It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the nth order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n. We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N.

Toward Exact Critical Exponents from the low-order loop expansion of the Effective Potential in Quantum Field Theory

The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1+1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a variational technique ( back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this work, we suggest a simple method of using the effective potential ( low order) to obtain exact values for the strong-coupling parameters for the ϕ4 scalar field theory in 0+1 and 1+1 space–time dimensions. For the 0+1 case, our results coincide with the well-known exact values already known from literature while for the 1+1 case we test the results by obtaining the corresponding exact critical exponent. As the effective potential is a well-established tool in quantum field theory, we expect that the results can be easily extended to the most important three dimensional case and then the dream of getting exact critical exponents is made possible.

Noether’s theorem and Ward-Takahashi identities from homotopy algebras

We derive the new identity in homotopy algebras which directly corresponds to the Schwinger-Dyson equations in quantum field theory. As an application, we derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi identities are reproduced in several examples. In general, our formula contains divergence. We mediate this problem by introducing stubs known in the context of string field theory. With the regularization, we can calculate the anomaly such as axial U(1) anomaly in vector-like U(1) gauge theory.

Noninvertible symmetries in 2D from type IIB string theory

We propose a top-down approach to noninvertible symmetries in two-dimensional quantum field theories and their three-dimensional (3D) associated symmetry topological field theories. We focus on the gauge theory engineered on D1-branes probing a particular Calabi-Yau 4-fold singularity. We show how to derive the symmetry topological field theory, a 3D Dijkgraaf-Witten theory, from the IIB supergravity under dimensional reduction. We also identify branes behind the noninvertible topological lines by dimensionally reducing their world volume actions. The action of noninvertible lines on charged local operators is then realized as the Hanany-Witten transition. Published by the American Physical Society 2024

Bridging Quantum Mechanics and Hydrogen Technology: The MEQ Framework

The quest for sustainable and renewable energy sources has become a paramount objective in the contemporary scientific and technological landscape. Amidst various alternatives, hydrogen emerges as a promising candidate, offering a clean, efficient, and versatile fuel option. However, the efficient and cost-effective production of hydrogen, particularly through water splitting, presents significant scientific and engineering challenges. This article delves into the innovative convergence of theoretical physics and practical engineering through the lens of the McGinty Equation (MEQ). The MEQ framework, a novel integration of quantum field theory and fractal potentials, proposes groundbreaking approaches to optimize the water-splitting process at the atomic and molecular levels. This exploration is not merely an academic exercise but a step towards tangible solutions in the pursuit of sustainable energy, with the MEQ playing a pivotal role in enhancing hydrogen production technologies.

Analyticity and the Unruh effect: a study of local modular flow

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

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

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

Solving the homogeneous Bethe-Salpeter equation with a quantum annealer

The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the GEVP by means of a quantum annealer, i.e., to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the simulated-annealing package and the D-Wave . The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. Published by the American Physical Society 2024

Holographic transport in anisotropic plasmas

We study energy-momentum and charge transport in strongly interacting holographic quantum field theories in an anisotropic thermal state by contrasting three different holographic methods to compute transport coefficients: standard holographic calculation of retarded Green’s functions, a method based on the null-focusing equation near horizon and the novel method based on background variations. Employing these methods we compute anisotropic shear and bulk viscosities and conductivities with anisotropy induced externally, for example by an external magnetic field. We show that all three methods yield consistent results. The novel method allows us to read off the transport coefficients from the horizon data and express them in analytic form from which we derive universal relations among them. Furthermore we extend the method based on the null-focusing equation to Gauss-Bonnet theory to compute higher derivative corrections to the aforementioned transport coefficients. Published by the American Physical Society 2024

Minimal-length quantum field theory: a first-principle approach

Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although few attempts at a quantum field-theoretical description of a minimal length has been proposed, they are rather the exception and there is no general agreement on the correct one. Here, using the quantum-mechanical model as a guidance, we propose a first-principle definition of a quantum field theory including a minimal length. Specifically, we propose a two-step procedure, by first describing the quantum-mechanical models as a classical field theory and subsequently quantizing it. We are thus able to provide a foundation for further exploration of the implications of a minimal length in quantum field theory.

Open AdS/CFT via a double-trace deformation

A concrete model of extracting the physics from the bulk of a gravitational universe is important to the study of quantum gravity and its possible relationship with experiments. Such a model can be constructed in the AdS/CFT correspondence by gluing a bath on the asymptotic boundary of the bulk anti-de Sitter (AdS) spacetime. This bath models a laboratory and is described by a quantum field theory. In the dual conformal field theory (CFT) description this coupling is achieved by a double-trace deformation that couples the CFT with the bath. This suggests that the physics observed by the laboratory is fully unitary. In this paper, we analyze the quantum aspects of this model in detail which conveys new lessons about the AdS/CFT correspondence, and we discuss the potential usefulness of this model in understanding subregion physics in a gravitational universe.

Quantum field theories of relativistic Luttinger fermions

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models. Published by the American Physical Society 2024

Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, (1) placing what was studied in [] for thermal quantum fields in the context of early universe cosmology, and (2) extending the considerations of vacuum compressibility of dynamical spaces treated in [] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using “in-in” techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution, where the in-thermal state and the out-thermal state are both well defined. Particle creation in the full history can then be calculated in this in-out asymptotically-stationary setup via the S-matrix transition amplitudes. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaître-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of these spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies. Published by the American Physical Society 2024

The Particle of Haag's Local Quantum Physics: A Critical Assessment.

Rudolf Haag's Local Quantum Physics (LQP) is an alternative framework to conventional relativistic quantum field theory for combining special relativity and quantum theory based on first principles, making it of great interest for the purposes of conceptual analysis despite currently being relatively limited as a tool for making experimental predictions. In LQP, the elementary particles are defined as species of causal link between interaction events, together with which they comprise its most fundamental entities. This notion of particle has yet to be independently assessed as such. Here, it is captured via a set of propositions specifying particle characteristics and then compared to previous particle notions. Haag's particle differs decisively with respect to mechanical intuitions about particles by lacking, among other things, even an approximate independent space-time location. This notion is thus found to differ greatly even from those of relativistic quantum mechanics and quantum field theory, which have been applied to the known elementary particles.

Defining geometric gauge theory to accommodate particles, continua, and fields

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates quantum electrodynamics. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism.

Three Cases of Complex Eigenvalue/Vector Distributions of Symmetric Order-Three Random Tensors

Abstract Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc., and studying their statistical properties, e.g. tensor eigenvalue/vector distributions, is interesting and useful. Recently some tensor eigenvalue/vector distributions have been computed by expressing them as partition functions of 0D quantum field theories. In this paper, using this method, we compute three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors, where the three cases can be characterized by the Lie-group invariances, $O(N,\mathbb {R})$, $O(N,\mathbb {C})$, and $U(N,\mathbb {C})$, respectively. Exact closed-form expressions of the distributions are obtained by computing partition functions of four-fermi theories, where the last case is of the “signed” distribution, which counts the distribution with a sign factor coming from a Hessian matrix. As an application, we compute the injective norm of the complex symmetric order-three random tensor in the large-N limit by computing the edge of the last signed distribution, obtaining agreement with an earlier numerical result in the literature.

Kinematic analysis of multiple Compton scattering in quantum-entangled two-photon systems

The Stokes–Mueller method is used to analyze the scattering of entangled photon pairs in a two-photon system. This study examines the scenario where one of the photons, part of a pair of maximally entangled annihilation photons, undergoes intermediate Compton scattering before both photons are detected using Compton polarimeters. The method also accounts for potential quantum-decoherence effects resulting from Compton scattering. The analysis investigates the scattering behavior in both parallel and perpendicular planes, identifying variations in the modulation factor that affect azimuthal correlations. These variations include increases, decreases, sign changes, or disappearances at certain intermediate scattering angles. This work aims to provide theoretical results that support the testing and verification of predictions made by quantum field theory.