General Field Theory Research Articles

On the Principle of Relativity of Inertia in Both General and Entangled Relativities

Entangled Relativity is a novel theory of relativity that offers a more economical approach than General Relativity. It successfully recovers both General Relativity and standard quantum field theory within a specific (yet generic) limit. Furthermore, Entangled Relativity precludes the existence of spacetime devoid of the matter that permeates it. Consequently, I argue that Entangled Relativity is not only preferable from the standpoint of Occam’s razor, due to its economical nature, but it also aligns more closely with Einstein’s original vision for a satisfactory theory of relativity.

Five-body D→V semileptonic decays

Our main objective is to derive the decay rate for the semileptonic decays D→Vℓ+νℓ(ℓ=e,μ), where V represents a vector particle. In these decays, the vector particle V decays into three pseudoscalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the D→ωℓ+νℓ, where ω subsequently decays into π+π−π0, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of D→ω form factors. These measurements can be performed using data obtained from BESIII. Published by the American Physical Society 2024

Emergence of String Monodromy in Effective Field Theory.

We demonstrate that when the field theory Kleiss-Kuijf and Bern-Carrasco-Johansson relations are imposed on one color ordering of general local bi-adjoint scalar effective field theories, the string monodromy relations must be obeyed by the other color ordering. This is a surprising example of an open string world-sheet property appearing in a purely field theoretic context. As part of the derivation, we show that nonlinear relations among the four-point Wilson coefficients arise from imposing linear symmetries on the six-point amplitude via factorization.

Causality and quasi-normal modes in the GREFT

The General Relativity Effective Field Theory (GREFT) introduces higher-derivative interactions to parameterise the gravitational effects of massive degrees of freedom which are too heavy to be probed directly. The coefficients of these interactions have recently been constrained using causality: both from the analytic structure of 4-point graviton scattering and the time delay of gravitational waves on a black hole background. In this work, causality is used to constrain the quasi-normal mode spectrum of GREFT black holes. Demanding that quasi-normal mode perturbations decay faster in the GREFT than in General Relativity—a new kind of causality condition which stems from the analytic structure of 2-point functions on a black hole background—leads to further constraints on the GREFT coefficients. The causality constraints and compact expressions for the GREFT quasi-normal mode frequencies presented here will inform future parameterised gravitational waveforms, and the observational prospects for gravitational wave observatories are briefly discussed.

Infrared finite scattering theory: scattering states and representations of the BMS group

Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an “out” state with memory which gives rise to infrared divergences in the standard S-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the “Lorentz orbit” of a given memory and classify all “orbit space representations” that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

The geometry of the solution space of first order Hamiltonian field theories I: From particle dynamics to free electrodynamics

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems – as a (0+1)-dimensional field – and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The general complex scalar field theory with a quadratic self-interaction term has been considered in the presence of a gravitational wave. The gravitational wave perturbation is then considered as a sum of discrete Fourier modes in the momentum space. Varying the action and making use of the principle of least action, one obtains two equations of motion corresponding to the gravitational perturbation and the time-dependent part of the pseudo-Goldstone boson. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonical commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. The entries of the covariance matrix now involves a stochastic contribution which results in an operatorial stochastic structure of the quantum Fisher information. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. It always has a finite value if the gravitons are initially in a squeezed state with high enough squeezing. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in a decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing. Published by the American Physical Society 2024

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

Identifying physics beyond SMEFT in the angular distribution of Λb→Λc(→Λπ)τν¯τ decay

In the Standard Model effective field theory (SMEFT), the SU(2)L×U(1)Y symmetry of the Standard Model is linearly realized. However, it is possible that more general effective field theories, such as the Higgs effective field theory (HEFT) where this symmetry is realized nonlinearly, are needed to describe the data. Identifying physics beyond SMEFT could shed light on the nature of Higgs and the realization of the electroweak symmetry. We explore the possibility of such an identification by studying the effects of scalar and vector new physics operators on the angular distribution of Λb→Λc(→Λπ)τν¯τ. This decay is sensitive to the six-dimensional effective operator OVLR≡(τ¯γμPLντ)(c¯γμPRb), which is present in HEFT but suppressed in SMEFT. We identify the angular observables that can have significant contributions from OVLR and hence would be useful for probing not only beyond the Standard Model physics but also physics beyond SMEFT. We further find that constraining the branching ratio of Bc→τν¯τ would be crucial for performing this task. Published by the American Physical Society 2024

Practical derivations of fermion and gauge boson reduction formulae in curved spacetimes

LSZ-type reduction formulae are derived for gauge fields and fermions in curved spacetime. The formulae are derived using a conserved current method applicable also to flat spacetimes. The method generalizes to more general quantum field theories. The formulae are then applied to a couple of basic problems to illustrate their use.

The Euclidean $\phi^{4}_{2}$ theory as a limit of an interacting Bose gas

We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction becomes small. The field theory is supported on distributions of negative regularity, which requires a renormalization by divergent mass and energy counterterms. We obtain convergence of the relative partition function and uniform convergence of the renormalized reduced density matrices. The proof is based on three main ingredients: (a) a quantitative analysis of the infinite-dimensional saddle point argument for the functional integral introduced by Fröhlich et al. (2022) using continuity properties of Brownian paths, (b) a Nelson-type estimate for a general nonlocal field theory in two dimensions, and (c) repeated Gaussian integration by parts in field space to obtain uniform control on the renormalized correlation functions. As a byproduct of our proof, in two and three dimensions we also extend the results on the mean-field limit by Fröhlich et al. (2022) and Lewin et al. (2021) to unbounded interaction potentials satisfying the optimal integrability conditions proposed by Bourgain (1997).

Compositional quantum field theory: An axiomatic presentation

We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of quantum field theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of general boundary quantum field theory, and is phrased in terms of correspondences between certain commuting diagrams of gluing identifications between manifolds and corresponding commuting diagrams of state-spaces and linear maps, thus making it amenable to formalization in terms of involutive symmetric monoidal functors and operad algebras. The underlying novel framework for gluing leads to equivariance of CQFT. We study CQFTs in dimension 2 and the algebraic structure they define on open and closed strings. We also consider, as a particular case, the compositional structure of 2-dimensional pure quantum Yang–Mills theory.

Generalized hidden conformal symmetry in quadratic f(T) gravity

We find the nonextremal charged rotating charged black holes in quadratic [Formula: see text] gravity are holographically dual to two different hidden conformal field theories. The two conformal field theories can be merged to find a very general hidden conformal field theory, which is generated by the [Formula: see text] modular group. We also carry out the calculation to the extremal limit of the black holes, and find the corresponding dual quantities. Contrary to the existence of two different dual conformal field theories for the extremal charged rotating black holes in Einstein gravity, we find only one dual theory exists for the extremal charged rotating black holes in quadratic [Formula: see text] gravity.

Junction conditions in a general field theory

It is well-known in the modified gravity scene that the calculation of junction conditions in certain complicated theories leads to ambiguities and conflicts between the various formulations. This paper introduces a general framework to compute junction conditions in any reasonable classical field theory and analyzes their properties. We prove that in any variational field theory, it is possible to define unambiguous and mathematically well-defined junction conditions either by interpreting the Euler–Lagrange differential equation as a distribution or as the extremals of a variational functional and these two coincide. We provide an example calculation which highlights why ambiguities in the existing formalisms have arisen, essentially due to incorrect usage of distributions. Relations between junction conditions, the boundary value problem of variational principles and Gibbons–Hawking–York-like surface terms are examined. The methods presented herein relies on the use of coordinates adapted to represent the junction surface as a leaf in a foliation and a technique for reducing the order of Lagrangians to the lowest possible in the foliation parameter. We expect that the reduction theorem can generate independent interest from the rest of the topics considered in the paper.

A heterotic Kodaira-Spencer theory at one-loop

We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like counter-terms. We also discuss the dependence on the background geometry, and in particular the choice of hermitian metric needed for quantisation. Given suitable topological constraints, this dependence may again be cancelled by the addition of purely background-dependent counter-terms. We also explain how our methods provide the one-loop partition functions of a large class of more general holomorphic field theories in terms of holomorphic Ray-Singer torsions.

General Fractional Noether Theorem and Non-Holonomic Action Principle

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory.

SMEFT is falsifiable through multi-Higgs measurements (even in the absence of new light particles)

By embedding the Standard Model effective field theory (SMEFT) in the more general Higgs effective field theory (HEFT), we expose correlations among the coefficients of the latter that, if found to be violated in future data, would lead to the experimental falsification of the SMEFT framework. These are derived from the necessary symmetric point of HEFT and analyticity of the SMEFT Lagrangian that allows the construction of the SMEFT expansion, as laid out by other groups, and properties at that point of the Higgs-flare function coupling Goldstone and Higgs bosons, of the Higgs potential V(h) and of the Higgs-top quark coupling function .

Thermal production of massless dark photons

A dark photon is predicted by several well-motivated Standard Model extensions and UV completions. Here the most general effective field theory up to dimension-six operatorsdescribing the interactions of a massless dark photon with all Standard Model particles is considered. This captures the predictions of a generic model featuring this type of vector boson at sufficiently low energies. In such framework the thermal production rate of dark photonsis computed at leading order, including the contributions of all SM particles. The corresponding cosmological yield of the dark photon and its contribution to the effective number of neutrinos are also calculated. These predictions satisfy the current observational bounds and will be tested by future measurements.

Scattering of evanescent particles

Massive Klein–Gordon theory is quantized on the timelike hypercylinder in Minkowski space. Crucially, not only the propagating, but also the evanescent sector of phase space is included, laying in this way foundations for a quantum scattering theory of fields at finite distance. To achieve this, the novel [Formula: see text]-Kähler quantization scheme is employed in the framework of general boundary quantum field theory. A potential quantization ambiguity is fixed by stringent requirements, leading to a unitary radial evolution. Formulas for building scattering amplitudes and correlation functions are exhibited. A novel LSZ formula is derived, applicable to scattering at finite distance.

Probing time orientability of spacetime

In general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics require these orientability assumptions is ultimately of observational or experimental nature, or the answer might come from a fundamental theory of physics. The possibility that spacetime is time non-orientable lacks investigation, and so should not be dismissed straightaway. In this paper, we argue that it is possible to locally access a putative time non-orientability of Minkowski empty spacetime by physical effects involving quantum vacuum electromagnetic fluctuations. We set ourselves to study the influence of time non-orientability on the stochastic motions of a charged particle subject to these electromagnetic fluctuations in Minkowski spacetime equipped with a time non-orientable topology and with its time orientable counterpart. To this end, we introduce and derive analytic expressions for a statistical time orientability indicator. Then we show that it is possible to pinpoint the time non-orientable topology through an inversion pattern displayed by the corresponding orientability indicator, which is absent when the underlying manifold is time orientable.