Local Quantum Field Research Articles

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

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.

Efficient vacuum-state preparation for quantum simulation of strongly interacting local quantum field theories

Efficient vacuum-state preparation for quantum simulation of strongly interacting local quantum field theories

Implications of a matter-antimatter mass asymmetry in Penning-trap experiments

The Standard Model (SM) of particle physics, being a local, unitary and Lorentz-invariant quantum field theory, remains symmetric under the combined action of Charge, Parity, and Time Reversal (CPT) symmetry. This automatically implies that fundamental properties of particles and antiparticles should be equal in magnitude. These fundamental tenets of the CPT principle have been put to stringent tests in recent Penning-trap experiments, where the matter-antimatter mass asymmetry has been measured. In light of these recent advances, we compare the bounds arising on CPT invariance from kaon systems with those from Penning-trap experiments. Using a simple yet powerful argument of mass decomposition of hadrons, we show that bounds on quark-antiquark mass differences from kaon oscillations are way beyond the reach of Penning-trap experiments. We lay out a roadmap to discuss possible reformulations of our understanding of the SM in the case of a discovery of CPT violation by these precision experiments.

A ‘black hole theorem,’ and its implications

A general formulation of the basic conflict of the information problem is given, encapsulated in a ‘black hole theorem.’ This is framed in a more general context than the usual one of quantum field theory on a background, and is based on describing a black hole as a quantum subsystem of a larger system, including its environment. This sharpens the limited set of possible consistent options; as with the Coleman-Mandula theorem, the most important point is probably the loophole in the ‘theorem,’ and what this tells us about the fundamental structure of quantum gravity. This ‘theorem’ in particular involves the general question of how to define quantum subsystems in quantum gravity. If black holes do behave as quantum subsystems, at least to a good approximation, evolve unitarily, and do not leave remnants, the ‘theorem’ implies the presence of interactions between a black hole and its environment that go beyond a description based on local quantum fields. This provides further motivation for and connects to previous work giving a principled parameterization of these interactions, and investigating their possible observational signatures via electromagnetic or gravitational wave observations of black holes.

Entanglement and separability in continuum Rokhsar-Kivelson states

We study a vast family of continuum Rokhsar-Kivelson (RK) states, which have their ground state encoded by a local quantum field theory. These describe certain quantum magnets, and are also important in quantum information. We prove the separability of the reduced density matrix of two disconnected subsystems, implying the absence of entanglement between the two subsystems---a stronger statement than the vanishing of logarithmic negativity. As a particular instance, we investigate the case where the ground state is described by a relativistic boson, which is relevant for certain magnets or Lifshitz critical points with dynamical exponent $z=2$, and we propose nontrivial deformations that preserve their RK structure. Specializing to 1D systems, we study a deformation that maps the ground state to the quantum harmonic oscillator, leading to a gap for the boson. We study the resulting correlation functions, and find that cluster decomposition is restored. We analytically compute the $c$ function for the entanglement entropy along a renormalization group flow for the wavefunction, which is found to be strictly decreasing as in CFTs. Finally, we comment on the relations to certain stoquastic quantum spin chains. We show that the Motzkin and Fredkin chains possess unusual entanglement properties not properly captured by previous studies.

Real-time observables from Euclidean thermal correlation functions

In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional renormalisation group in the quark-meson model, we demonstrate that in-medium effects can be directly extracted from the spatial momentum dependence of the Euclidean propagators, in contrast to conventional approaches, which rely on the reconstruction from different Matsubara frequencies. As an application, we determine the analytic features that arise from the discrete spectral contribution to the pion correlation function, and calculate the non-perturbative shear viscosity arising from these states.

Euclidean thermal correlation functions in local QFT

In this work we outline the general analytic characteristics satisfied by scalar correlation functions at finite temperature in local quantum field theory. We demonstrate that the locality of the fields in particular imposes significant constraints on the spectral structure of the theory, and that this enables the non-perturbative effects experienced by thermal particle states to be directly calculated from Euclidean correlation functions, avoiding the inverse problem.

On the questions of asymptotic recoverability of information and subsystems in quantum gravity

A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of solving the gravitational constraints appear to imply that the answers to this question here are different than in finite quantum systems, or in local quantum field theory. Specifically, the constraints can be solved by providing a “gravitational dressing” for the underlying field-theory operators, but this modifies their locality properties. It has been argued that holography itself may be explained through this role of the gauge symmetry and constraints, at the nonperturbative level, but there are also subtleties in constructing a holographic map in this approach. There are also claims that holography is implied even by perturbative solution of the constraints. This short note provides further examination of these questions, and in particular investigates to what extent perturbative or nonperturbative solution of the constraints implies that information naïvely thought to be localized can be recovered by asymptotic measurements, and the relevance of this in defining subsystems. In the leading perturbative case, the relevant effects are seen to be exponentially suppressed and asymptotically vanishing, for massive fields. These questions are, for example, important in sharply characterizing the unitarity problem for black holes.

Uncertainties in quantum measurements: a quantum tomography

The observables associated with a quantum system S form a non-commutative algebra . It is assumed that a density matrix ρ can be determined from the expectation values of observables. But admits inner automorphisms , , so that its individual elements can be identified only up to unitary transformations. So since Tr ρ(uau*) = Tr(u*ρu)a, only the spectrum of ρ, or its characteristic polynomial, can be determined in quantum mechanics. In local quantum field theory, ρ cannot be determined at all, as we shall explain. However, abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables in abelian algebras (M for measurement, S for system). We study the uncertainties in extending to (the determination of which means measurement of ) and devise a protocol to determine by determining for different choices of . The problem we formulate and study is a generalization of the Kadison–Singer theorem. We give an example where the system S is a particle on a circle and the experiment measures the abelian algebra of a magnetic field B coupled to S. The measurement of B gives information about the state ρ of the system S due to operator mixing. Associated uncertainty principles for von Neumann entropy are discussed in the appendix, adapting the earlier work by Białynicki-Birula and Mycielski (1975 Commun. Math. Phys. 44 129) to the present case.

Some Aspects About Pushing the CPT and Lorentz Invariance Frontier With Neutrinos

The CPT symmetry, which combines Charge Conjugation, Parity, and Time Reversal, is a cornerstone of our model-building method, and its probable violation will endanger the most extended tool we presently utilize to explain physics, namely local relativistic quantum fields. However, the kaon system’s conservation constraints appear to be rather severe. We will show in this paper that neutrino oscillation experiments can enhance this limit by many orders of magnitude, making them an excellent instrument for investigating the basis of our understanding of Nature. As a result, verifying CPT invariance does not evaluate a specific model, but rather the entire paradigm. Therefore, as the CPT’s status in the neutrino sector, linked or not to Lorentz invariance violation, will be assessed at an unprecedented level by current and future long baseline experiments, distinguishing it from comparable experimental fingerprints coming from non-standard interactions is critical. Whether the entire paradigm or simply the conventional model of neutrinos is at jeopardy is significantly dependent on this.

A thermodynamic origin for the Cohen-Kaplan-Nelson bound

The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent r used in the text). We deduce that the CKN bound is one possible solution to this extremization problem (with ), but there are others consistent with r = 2. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

Continuous entanglement renormalization on the circle

The continuous multiscale entanglement renormalization ansatz (cMERA) is a variational class of states for quantum fields. As originally formulated, the cMERA applies to infinite systems only. In this paper we generalize the cMERA formalism to a finite circle, which we achieve by wrapping the action of the so-called entangler around the circle. This allows us to transform a cMERA on the line into a cMERA on the circle. In addition, in the case of a Gaussian cMERA for noninteracting quantum fields, the method of images allows us to prove the following result: If on the line a cMERA state is a good approximation to a ground state of a local quantum field theory (QFT) Hamiltonian, then (under mild assumptions on their correlation functions) the resulting cMERA on a circle is also a good approximation to the ground state of the same local QFT Hamiltonian on the circle.

Spectral representation of the shear viscosity for local scalar QFTs at finite temperature

In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.

Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions

We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.

Holographic complexity of LST and single trace Toverline{T}

In this work, we continue our study of string theory in the background that interpolates between AdS3 in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a CFT2 in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study computational complexity of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of complexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case.

Thermodynamics from relative entropy.

Thermodynamics can be developed from a microscopic starting point in terms of entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example, in the context of local quantum field theory. We find that the principle of maximum entropy can be replaced by a principle of minimum expected relative entropy. Various ensembles and their thermodynamic potentials can be defined through relative entropy. We also show that thermal fluctuations are in fact governed by a relative entropy. Furthermore, we reformulate the third law of thermodynamics using relative entropy only.

Octonions, trace dynamics and noncommutative geometry—A case for unification in spontaneous quantum gravity

Abstract We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics and Connes noncommutative geometry program. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic—together they describe an ‘aikyon’. The Lagrangian of the theory is invariant under global unitary transformations and describes gravity and Yang–Mills fields coupled to fermions. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group G 2 which has 14 generators [could they stand for the 12 vector bosons and two degrees of freedom of the graviton?]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally and could lead to a unification of gravity with the standard model. From this matrix dynamics, local quantum field theory arises as a low energy limit of this Planck scale dynamics of aikyons, and classical general relativity arises as a consequence of spontaneous localisation of a large number of entangled aikyons. We propose that classical curved space–time and Yang–Mills fields arise from an effective gauging which results from the collection of symmetry groups of the spontaneously localised fermions. Our work suggests that we live in an eight-dimensional octonionic universe, four of these dimensions constitute space–time and the other four constitute the octonionic internal directions on which the standard model forces live.

Gravity, Superselection Rules and Axions

AbstractIt is generally accepted that consistent coupling to quantum gravity implies that any low energy free parameter is in reality the vacuum expectation value of some local quantum field. In this note we present a modest attempt to prove this general claim using as key example the θ parameter of QCD and the Peccei‐Quinn axion solution of the strong CP problem. The gravitational emergence of the local axion field associated with the superselection θ parameter is worked out using as basic ingredients the quantum representation of classical geometries in terms of coherent states and the interpretation of the θ QCD superselection rule in quantum information terms as the lack of a quantum reference frame for topological charge. The formal connection with the model independent axion in string theory is briefly discussed.

Towards a Unitary, Renormalizable, and Ultraviolet-Complete Quantum Theory of Gravity

For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry which derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Ho\v{r}ava gravity, a quantum Lifshitz field theory of gravity characterized by an anisotropic scaling between space and time, unitarity and renormalizability can be retained while Lorentz invariance is sacrificed at high energies and must emerge only as approximate symmetry at low energies. I review various approaches to perturbative quantum gravity with a particular focus on recent progress in the quantization of Ho\v{r}ava gravity, supporting its theoretical status as a unitary, renormalizable and ultraviolet-complete quantum theory of gravity.