Formulation Of Field Theory Research Articles

Time-symmetric quantization of relativistic fields. 2. Electroweak theory. Observable effects of TSQ

In the method of time-symmetric quantization (TSQ) of relativistic systems, based on the Stückelberg-Feynman interpretation, the creation-annihilation operators of quanta of complex fields and massless gauge fields, are automatically normally ordered, and there is no vacuum energy and charge (Z. Zakir 2023, article 1). In this second article the application of TSQ to massive bosonic fields of electroweak theory and the observational consequences of TSQ are considered. It is shown that the vacuum of these fields is free of zero-point energy and zero-point charge, and thus a contribution of these fields to the cosmological constant is absent. A direct observational consequence of TSQ is crossing symmetry in particle physics. The observable effects, which were attributed to the zero-point energy of the vacuum, are actually generated by the fields of real charges, and there is no evidence of the existence of zero-point energy of fundamental fields. This fact contradicts the prediction of the standard formulation of quantum field theory, but indirectly confirms TSQ.

A Rigorous Derivation of the Functional Renormalisation Group Equation

The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder–Schrader formulation of quantum field theory. To this end, we devise a very general regularisation scheme which retains reflection positivity as well as the infinite degrees of freedom including smoothness. Furthermore, it is shown how the classical limit is altered by the regularisation process leading to an inevitable breaking of translation invariance. We also give precise conditions for the convergence of the obtained theories upon removal of the regularisation.

Third quantization of open quantum systems: Dissipative symmetries and connections to phase-space and Keldysh field-theory formulations

Third quantization of open quantum systems: Dissipative symmetries and connections to phase-space and Keldysh field-theory formulations

Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity

We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time τ, on a compact space manifold Ω. We explain how to compute the evolution operator U(tf, ti) between the initial time ti and the final time tf = ti + τ, study unitarity and renormalizability, and show how to include purely virtual particles, by rendering some physical particles (and all the ghosts, if present) purely virtual. The details about the restriction to finite τ and compact Ω are moved away from the internal sectors of the diagrams (apart from the discretization of the three-momenta), and coded into external sources. Unitarity is studied by means of the spectral optical identities, and the diagrammatic version of the identity U†(tf, ti)U(tf, ti) = 1. The dimensional regularization is extended to finite τ and compact Ω, and used to prove, under general assumptions, that renormalizability holds whenever it holds at τ = ∞, Ω = ℝ3. Purely virtual particles are introduced by removing the on-shell contributions of some physical particles, and the ghosts, from the core diagrams, and trivializing their initial and final conditions. The resulting evolution operator Uph(tf, ti) is unitary, but does not satisfy the more general identity Uph(t3, t2)Uph(t2, t1) = Uph(t3, t1). As a consequence, Uph(tf, ti) cannot be derived from a Hamiltonian in a standard way, in the presence of purely virtual particles.

Leptonic Decay Widths for the Composite System of Two Relativistic Fermions

The new relativistic semiclassical leptonic decay widths of vector mesons as the relativistic systems of two quarks with arbitrary masses interacting by means of the funnel-type potentials with Coulomb interaction are obtained. The behavior of the relativistic leptonic decay widths of vector mesons is investigated. Comparison of the behavior for new expression with its relativistic spinless analog is given. Consideration is conducted within the framework of completely covariant quasipotential approach in the Hamiltonian formulation of quantum field theory via a transition to the relativistic configurational representation in the case of two relativistic spin particles of arbitrary masses.

Search for the production of dark matter candidates in association with heavy dimuon resonance using the CMS open data for proton–proton collisions at sqrt{s} = 8 TeV

In this work, we present a search for the possible production of Dark Matter particles at the Large Hadron Collider alongside a new hypothetical neutral gauge boson denoted by {Z}^{prime }. The topology of the studied events is dimuons plus large missing transverse momentum. The study is performed using the CMS open data samples collected by the CMS experiment in the LHC proton–proton collisions at center-of-mass energy of 8 TeV in 2012, which corresponds to an integrated luminosity of 11.6 hbox {fb}^{-1}, and the corresponding CMS open Monte Carlo samples. Two benchmark scenarios were used for interpreting the data, the Dark Higgs scenario and the effective field theory formalism. No evidence for the existence of dark matter candidates was found. 95% confidence level limits are set on the masses of the {Z}^{prime } and the cutoff scale of the effective field theory.

What quantum matter tells about quantisation of gravity in a statistical mechanics context

We propose a “guide” towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space. On the other hand, the path integral formulation of quantum field theory can be interpreted from the point of view of statistical mechanics. From these perspectives, gravity and matter are related to each other in the same way as a gas and its chemical potential are. This statistical mechanics interpretation of gravity and matter suggests that gravity should be quantised in a precise way which is determined by the quantisation of matter. Although, in a first step, quantisation of gravity applies for small perturbations of the metric with respect to the vacuum, the most central and general features of quantisation (quantisation prescription, quantum space dimensions) are supported from statistical mechanics and remain valid non-perturbatively.

Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel

The complex Langevin (CL) method is a promising approach to overcome the sign problem that occurs in real-time formulations of quantum field theories. Using the Schwinger-Keldysh formalism, we study SU(Nc) gauge theories with CL. We observe that current stabilization techniques are insufficient to obtain correct results. Therefore, we revise the discretization of the CL equations on complex time contours, find a time reflection symmetric formulation and introduce a novel anisotropic kernel that enables CL simulations on discretized complex time paths. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that we validate using additional observables and that can be systematically improved. For the first time, we are able to simulate non-Abelian gauge theory on time contours whose real-time extent exceeds its inverse temperature. Thus, our approach may pave the way towards an ab-initio real-time framework of QCD in and out of equilibrium with a potentially large impact on the phenomenology of heavy-ion collisions.

Prospects of testing late-time cosmology with weak lensing of gravitational waves and galaxy surveys

We investigate the synergy of upcoming galaxy surveys and gravitational wave (GW) experiments in constraining late-time cosmology, examining the cross-correlations between the weak lensing of gravitational waves (GW-WL) and the galaxy fields. Without focusing on any specific GW detector configuration, we benchmark the requirements for the high precision measurement of cosmological parameters by considering several scenarios, varying the number of detected GW events and the uncertainty on the inference of the source luminosity distance and redshift.We focus on ΛCDM and scalar-tensor cosmologies, using the Effective Field Theory formalism as a unifying language. We find that, in some of the explored setups, GW-WL contributes to the galaxy signal by doubling the accuracy on non-ΛCDM parameters, allowing in the most favourable scenarios to reach even percent and sub-percent level bounds. Though the most extreme cases presented here are likely beyond the observational capabilities of currently planned individual GW detectors, we show nonetheless that — provided that enough statistics of events can be accumulated — GW-WL offers the potential to become a cosmological probe complementary to LSS surveys, particularly for those parameters that cannot be constrained by other GW probes such as standard sirens.

Non-Abelian gauge structure and flavor mixing in quantum field theory1

The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.

The shadow formalism of Galilean CFT2

In this work, we develop the shadow formalism for two-dimensional Galilean conformal field theory (GCFT2). We define the principal series representation of Galilean conformal symmetry group and find its relation with the Wigner classification, then we determine the shadow transform of local operators. Using this formalism we derive the OPE blocks, Clebsch-Gordan kernels, conformal blocks and conformal partial waves. A new feature is that the conformal block admits additional branch points, which would destroy the convergence of OPE for certain parameters. We establish another inversion formula different from the previous one, but get the same result when decomposing the four-point functions in the mean field theory (MFT). We also construct a continuous series of bilocal actions of MFT, and an exceptional series of local actions, one of which is the BMS free scalar model. We notice that there is an outer automorphism of the Galilean conformal symmetry, and the GCFT2 can be regarded as null defect in higher dimensional CFTs.

Time-symmetric quantization of relativistic fields. 1. Complex fields, massless gauge fields and gravitons

In the standard formulation of quantum field theory (QFT), where there are only positive energy particles and antiparticles, the energy and charge of the vacuum diverge, which, due to the existence of gravity, leads to the inconsistency of the theory (cosmological constant problem). In the article, it is shown that in the Stueckelberg-Feynman (SF) interpretation, where antiparticles are described as negative energy particles moving backward in time, the zero-point energy and zero-point charge of vacuum of complex fields are absent and there is no cosmological constant problem. However, until now it was believed that the SF interpretation leads to negative probabilities and incompatible with QFT. In the article, it is presented a new formulation of QFT on the basis of the SF interpretation in the form of time-symmetric quantization (TSQ), where the probability of states is positive. In TSQ, the consequences of the SF interpretation are taken into account consecutively and it is shown that: a) the negative sign of the norm of states only changes the sign of the wave function, and not the probabilities; b) the expression of backward in time integrals through the forward in time integrals changes sign; c) the time ordering of the operators is symmetric in time and writing them through the usual ordering leads to the standard diagram technique. For this reason, TSQ correctly describes the known observable effects. In TSQ, the results of unification models change, in particular, a) there is no zero-point energy even with broken supersymmetry between complex fields; b) there is no zero-point energy of modes in string theories, which allows to include gravity, but there is no a conformal anomaly and the dimension of space can be arbitrary.

Framed 𝔼n-algebras from quantum field theory

This paper addresses the following question: given a topological quantum field theory on [Formula: see text] built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented n-manifold? We study a broad class of topological field theories — those of AKSZ type — and obtain an explicit condition for the vanishing of the framing anomaly, i.e. the obstruction to performing this globalization procedure. We also interpret our results in terms of identifying the observables as an algebra over the framed little n-disks operad. Our analysis uses the BV formalism for perturbative field theory and the notion of factorization homology.

Anomalous dimensions from soft Regge constants

Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of 2 → 2 scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to mathcal{O} (ϵ) in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e. the terms sim {alpha}_s^{k+1}{n}_f^k for any k, where nf is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.

Addressing energy density functionals in the language of path-integrals I: comparative study of diagrammatic techniques applied to the (0 + 0)-D O(N)-symmetric $$\varphi ^{4}$$-theory

The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral formulation of quantum field theory. The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present below a comparative study of such techniques applied to a toy model, i.e. the (0 + 0)-D O(N)-symmetric $$\varphi ^{4}$$ -theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion, optimized perturbation theory and self-consistent perturbation theory. With these methods, we notably address the spontaneous breakdown of the O(N) symmetry with care especially since spontaneous symmetry breakings play a paramount role in current implementations of the EDF approach.

Differential toverline{t} cross-section measurements using boosted top quarks in the all-hadronic final state with 139 fb−1 of ATLAS data

Measurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13 TeV proton–proton collisions recorded by the ATLAS detector at the LHC. The top quarks are observed through their hadronic decay and reconstructed as large-radius jets with the leading jet having transverse momentum (pT) greater than 500 GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the toverline{t}to WWboverline{b} branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have pT> 500 GeV and pT> 350 GeV, respectively, is 331 ± 3(stat.) ± 39(syst.) fb. This is approximately 20% lower than the prediction of {398}_{-49}^{+48} fb by Powheg+Pythia 8 with next-to-leading-order (NLO) accuracy but consistent within the theoretical uncertainties. Results are also presented at the parton level, where the effects of top-quark decay, parton showering, and hadronization are removed such that they can be compared with fixed-order next-to-next-to-leading-order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase space similar to that at particle level, is 1.94 ± 0.02(stat.) ± 0.25(syst.) pb. This agrees with the NNLO prediction of {1.96}_{-0.17}^{+0.02} pb. Reasonable agreement with the differential cross-sections is found for most NLO models, while the NNLO calculations are generally in better agreement with the data. The differential cross-sections are interpreted using a Standard Model effective field-theory formalism and limits are set on Wilson coefficients of several four-fermion operators.

Binary dynamics from worldline QFT for scalar QED

We investigate the worldline quantum field theory (WQFT) formalism for scalar QED and observe that a generating function emerges from WQFT, from which the scattering angle ensues. This generating function bears important similarities to the radial action in that it requires no consideration of exponentiation of lower-order contributions. We demonstrate the computations of this generating function and the resulting scattering angle of a binary system coupled to an electromagnetic field up to the third order in the post-Minkowskian expansion.

Renormalization of nuclear chiral effective field theory with nonperturbative leading-order interactions

We extend the renormalizability study of the formulation of chiral effective field theory with a finite cutoff, applied to nucleon-nucleon scattering, by taking into account non-perturbative effects. We consider the nucleon-nucleon interaction up to next-to-leading order in the chiral expansion. The leading-order interaction is treated non-perturbatively. In contrast to the previously considered case when the leading-order interaction was assumed to be perturbative, new features related to the renormalization of the effective field theory are revealed. In particular, more severe constraints on the leading-order potential are formulated, which can enforce the renormalizability and the correct power counting for the next-to-leading order amplitude. To illustrate our theoretical findings, several partial waves in the nucleon-nucleon scattering, $^3P_0$, $^3S_1-{^3D_1}$ and $^1S_0$ are analyzed numerically. The cutoff dependence and the convergence of the chiral expansion for those channels are discussed.

A consistent quantum field theory from dimensional reduction

We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory (QFT). In this new framework, space and momentum integrations are modified by a weighting function incorporating an effective mass energy associated with the dimensional reduction scale. We quantize the theory within canonical formalism. We then show that it can be made finite in perturbation theory, free of renormalon ambiguities, and with better analytic behavior for infinitesimal coupling constant compared to standard QFT. The new approach reproduces the known results at low energies. One key feature of this class of models is that the coupling constant always reaches a fixed point in the ultraviolet (UV) region, making the models UV complete.

Inclusive production of J/ψ, ψ(2S), and Υ states in pNRQCD

Under some assumptions on the hierarchy of relevant energy scales, we compute the nonrelativistic QCD (NRQCD) long-distance matrix elements (LDMEs) for inclusive production of J/ψ, ψ(2S), and Υ states based on the potential NRQCD (pNRQCD) effective field theory. Based on the pNRQCD formalism, we obtain expressions for the LDMEs in terms of the quarkonium wavefunctions at the origin and universal gluonic correlators, which do not depend on the heavy quark flavor or the radial excitation. This greatly reduces the number of nonperturbative unknowns and substantially enhances the predictive power of the nonrelativistic effective field theory formalism. We obtain improved determinations of the LDMEs for J/ψ, ψ(2S), and Υ states thanks to the universality of the gluonic correlators, and obtain phenomenological results for cross sections and polarizations at large transverse momentum that agree well with measurements at the LHC.