Lorentz-invariant Theory Research Articles

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time MJ1,3, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

We present a gauge and Lorentz invariant effective field theory model for the interaction of a charged scalar matter field with a magnetic monopole source, described by an external magnetic current. The quantum fluctuations of the monopole field are described effectively by a strongly coupled “dual” Ud(1) gauge field, which is independent of the electromagnetic Uem(1) gauge field. The effective interactions of the charged matter with the monopole source are described by a gauge invariant mixed Chern-Simons-like (Pontryagin-density) term between the two U(1) gauge fields. The latter interaction coupling is left free, and a lattice study of the system is performed with the aim of determining the phase structure of this effective theory. Our study shows that, in the spontaneously broken-symmetry phase, the monopole source triggers, via the mixed Chern-Simons term, which is nontrivial in its presence, the generation of a dynamical singular configuration (magnetic-monopolelike) for the respective gauge fields. The scalar field also behaves in the broken phase in a way similar to that of the scalar sector of the ’t Hooft-Polyakov monopole. Moreover, we show that the modest size of the lattices involved does not have significant effects on the main conclusions of our analysis. Published by the American Physical Society 2024

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.

Trirefringence and the M5-brane

The Hamiltonian formulation for nonlinear chiral 2-form electrodynamics in six-dimensional Minkowski spacetime is used to show that small-amplitude plane-wave perturbations of a generic uniform constant ‘magnetic’ background exhibit trirefringence: all three independent wave-polarisations have distinct dispersion relations. While two coincide for Lorentz invariant theories, all three coincide uniquely for the chiral 2-form theory on the worldvolume of the M5-brane of M-theory. We argue that this is because, in this M-theory context, the waves propagate in a planar M5-M2-M2 bound-state preserving 16 supersymmetries. We also show how our results imply analogous results for nonlinear electrodynamics in a Minkowski spacetime of five and four dimensions.

To Half-Be or Not To Be?

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

The Analytic Wavefunction

The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an off-shell wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.

On photonic tunnelling and the possibility of superluminal transport of electromagnetic energy

Motivated by the increased interest in experiments in which light appears to propagate by tunnelling at superluminal velocity, the Lorentz invariant theory proposed by Partha Ghose to explain these surprising effects is revisited. This theory is based on the Harish-Chandra formalism, which describes the relativistic dynamics of a massless spin-1 boson, like a photon. By this formalism, the Bohmian average transport velocity of the electromagnetic energy is formulated. It is proved that this velocity can be superluminal if the dielectric making the waveguide is non-absorptive and non-dispersive. This result is validated in the framework of quantum electrodynamics, demonstrating that the average velocity of the photon inside the waveguide is given by the contribution of instantaneous superluminal velocities. This theory, therefore, suggests the optimal conditions for designing the optical devices capable of locally transporting electromagnetic energy at superluminal velocities mitigating signal attenuation.

Casimir effect in DFR space–time

Noncommutative space–time introduces a fundamental length scale suggested by approaches to quantum gravity. Here, we report the analysis of the Casimir effect for parallel plates separated by a distance of [Formula: see text] using a Lorentz invariant scalar theory in a noncommutative space–time (DFR space–time), both at zero and finite temperatures. This is done in two ways; one when the additional space-dimensions introduced in DFR space–time are treated as extra dimensions but on par with usual space-dimension and in the second way, the additional dimensions are treated as compact dimensions. Casimir force obtained in the first approach coincides with the result in the extra-dimensional commutative space–time and this is varying as [Formula: see text]. In the second approach, we derive the corrections to the Casimir force, which is dependent on the separation between the plate, [Formula: see text] and on the size of the extra compactified dimension, [Formula: see text]. Since correction terms are very small, keeping only the most significant terms of these corrections, we show that for certain values of the [Formula: see text], the corrections due to noncommutativity make the force between the parallel plates more attractive, and using this, we find lower bound on the value of [Formula: see text]. We show here that the requirement of the Casimir force and the energy to be real impose the condition that the weight function used in defining the DFR action has to be a constant. At zero temperature, we find correction terms due to noncommutativity depend on [Formula: see text]- and [Formula: see text]-dependent modified Bessel functions [Formula: see text] and [Formula: see text], with coefficients that vary as [Formula: see text] and [Formula: see text], respectively. For finite temperature, the Casimir force has correction terms that scale as [Formula: see text] and [Formula: see text] in high-temperature limit and as [Formula: see text] and [Formula: see text] in the low-temperature limit.

Probing Lorentz violation at ultra-high energies using air showers

In air showers initiated by ultra-high-energy cosmic rays in the Earth’s atmosphere, even the secondary particles created in the start-up phase are produced at energies far above those accessible by other means. These high-energy particles can be used to search for New Physics, such as a violation of Lorentz invariance. We focus on isotropic, nonbirefringent Lorentz violation in the photon sector and consider the two cases κ < 0 and κ > 0 (i.e., the velocity of photons is larger/smaller than the maximum attainable velocity of standard Dirac fermions). In both cases, processes that are forbidden in the standard, Lorentz-invariant theory (κ = 0) become allowed, in particular photon decay in the case κ < 0 and vacuum-Cherenkov radiation for κ > 0. Implementing these processes into air-shower simulations, we found that the development of an air shower at the highest energies can be significantly impacted, specifically the average atmospheric depth of the shower maximum X max and its shower-to-shower fluctuations σ(X max). Comparing these simulations to actual measurements, we were able to obtain much stricter bounds on this specific type of LV in the case κ < 0 than possible with previous methods. We discuss these limits and, in addition, present first results for the case κ > 0.

Unruh-Fulling effect in nonlocal field theory: The role of Unruh decomposition

We investigate the Unruh-Fulling effect in a class of nonlocal field theories by examining both the number operator and Unruh-DeWitt detector methods. Unlike in previous literature, we use Unruh quantization to quantize the matter field. Such choice, as oppose to standard Minkowski decomposition, naturally incorporates the time translational invariance in the positive frequency Wightman function and thus captures the thermal equilibrium of the system. We analyze the Unruh-Fulling effect for a massless real scalar field in both the Lorentz noninvariant and Lorentz invariant nonlocal theories. In Lorentz noninvariant nonlocal theory, the expectation value of number operator and the response function of the detector are modified by an overall multiplicative factor. Whereas in Lorentz invariant nonlocal theory these quantities remain identical to those of the standard Unruh-Fulling effect. The temperature of the thermal bath remains unaltered for both the Lorentz noninvariant and Lorentz invariant nonlocal theories. Therefore, in terms of temperature, the nonlocal Unruh-Fulling effect is universal while it is derived via Unruh quantization, whereas the transition rate may be modified.

Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: Peripheral phases

We study the nucleon-nucleon interaction up to next-to-next-to-leading order using time-ordered perturbation theory in the framework of manifestly Lorentz-invariant chiral effective field theory. We present the two-pion exchange contribution at one-loop level, which is consistent with the corresponding non-relativistic expressions in the large-nucleon-mass limit. Using the Born series truncated at one-loop order, we calculate the phase shifts and mixing angles of the partial waves with the angular momentum $l\geq 2$. Comparing with the results of non-relativistic formulation, we find an improved description of the phase shifts for some $D$ waves such as the $^3D_3$ one. For the other partial waves, both approaches show the globally similar results.

Radiative correction to lepton proton scatterings in manifestly Lorentz-invariant chiral perturbation theory

Manifestly lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at next-to-leading order with nonzero lepton mass, in which both are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model, but somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry.

Operators for generic effective field theory at any dimension: on-shell amplitude basis construction

We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT (Amplitude Basis Construction for Effective Field Theories).

Ghost and tachyon free propagation up to spin 3 in Lorentz invariant field theories

We complete the set of spin-projector operators for fields up to rank-3 by providing all operators connecting sectors with same spin and parity. In this way we can broaden the search for unitary and non-tachyonic particle propagation in quadratic lagrangian with inter-field mixing. We use the properties of projector algebra to reanalyze known theories and shed light towards new healthy ones. We do so with full control over the gauge constraints by working the form of the saturated propagator in an appropriate frame of reference.

Moffat\u2019s modified gravity tested on X-COP galaxy clusters

Scalar tensor vector gravity (STVG) is a fully covariant Lorentz invariant alternative theory of gravity also known as MOdified Gravity (MOG) which modifies General Relativity by inclusion of dynamical massive vector field and scalar fields. In STVG the mass mu of the vector field phi _{mu } and the gravitational constant G acquire the status of dynamical fields. We use the reconstructed total cluster mass of the X-COP sample obtained from X-ray observations by XMM-Newton telescope in combination with Sunyaev–Zel’dovich (SZ) effect observed within Planck all-sky survey to estimate the alpha and mu parameters of MOG theory. The obtained values are consistent with previous fits by other authors. Hence the MOG is passing another test and proves its consistency strengthening thereby its stance of being a promising alternative to General Relativity.

On Lorentz Invariant Complex Scalar Fields

We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, Ψ x ⟶ e i / ℏ f x Ψ x . We show that the spacetime-dependent phase f x is the most natural relativistic extension of the phase associated with the transformation rule for the nonrelativistic Schrödinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that Ψ x transforms according to the above rule under proper Lorentz transformations (boosts or spatial rotations). This is the most general transformation rule compatible with a Lorentz invariant physical theory whose observables are bilinear functions of the field Ψ x . We use the previous wave equations to describe several physical systems. In particular, we solve the bound state and scattering problems of two particles which interact both electromagnetically and gravitationally (static electromagnetic and gravitational fields). The former interaction is modeled via the minimal coupling prescription while the latter enters via an external potential. We also formulate logically consistent classical and quantum field theories associated with these Lorentz covariant wave equations. We show that it is possible to make those theories equivalent to the Klein-Gordon theory whenever we have self-interacting terms that do not break their Lorentz invariance or if we introduce electromagnetic interactions via the minimal coupling prescription. For interactions that break Lorentz invariance, we show that the present theories imply that particles and antiparticles behave differently at decaying processes, with the latter being more unstable. This suggests a possible connection between Lorentz invariance-breaking interactions and the matter-antimatter asymmetry problem.

Should Unstable Quantum Field Theories be Lorentz-invariant?

An unstable field theory is what we obtain when we linearise the equations of an interacting field theory near an unstable state. Theories of this kind are adopted to model the onset of spontaneous symmetry breakings, when the fields are sitting on the top of the Mexican hat, and they start to ''roll down'' to the bottom. At present, there exists no rigorous proof that unstable quantum field theories are Lorentz-invariant (in the sense of Wigner's theorem). Here, we show that they shouldn't be. In fact, unstable theories always have a limited regime of applicability, and they are valid only for a very short time. As consequence, there is a preferred simultaneity hyperplane, along which the unstable theory is everywhere applicable, while a generic observer (whose four-velocity is not orthogonal to such hyperplane) must use the full non-linear theory. In summary: the current quantization schemes are ''ok'', independently from whether they lead to a Lorentz-invariant theory.

Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence

Quantisation of Lorentz invariant scalar field theory in Doplicher-Fredenhagen-Roberts (DFR) space-time, a Lorentz invariant, non-commutative space-time is studied. We use an approach to quantisation that is based on the equations of motion alone and derive the equal time commutation relation between Doplicher-Fredenhagen-Roberts-Amorim (DFRA) scalar field and its conjugate, which has non-commutative dependent modifications, but the corresponding creation and annihilation operators obey usual algebra. We show that imposing the condition that the commutation relation between the field and its conjugate is same as that in the commutative space-time leads to a deformation of the algebra of quantised oscillators. Both these deformed commutation relations derived are valid to all orders in the non-commutative parameter. By analysing the first non-vanishing terms which are θ3 order, we show that the deformed commutation relations scale as 1/λ4, where λ is the length scale set by the non-commutativity of the space-time. We also derive the conserved currents for DFRA scalar field. Further, we analyse the effects of non-commutativity on Unruh effect by analysing a detector coupled to the DFRA scalar field, showing that the Unruh temperature is not modified but the thermal radiation seen by the accelerated observer gets correction due to the non-commutativity of space-time.

Carroll contractions of Lorentz-invariant theories

We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.

Toward a Mechanism for the Emergence of Gravity

One of the main problems that emergent-gravity approaches face is explaining how a system that does not contain gauge symmetries ab initio might develop them effectively in some regime. We review a mechanism introduced by some of the authors for the emergence of gauge symmetries in [JHEP 10 (2016) 084] and discuss how it works for interacting Lorentz-invariant vector field theories as a warm-up exercise for the more convoluted problem of gravity. Then, we apply this mechanism to the emergence of linear diffeomorphisms for the most general Lorentz-invariant linear theory of a two-index symmetric tensor field, which constitutes a generalization of the Fierz–Pauli theory describing linearized gravity. Finally we discuss two results, the well-known Weinberg–Witten theorem and a more recent theorem by Marolf, that are often invoked as no-go theorems for emergent gravity. Our analysis illustrates that, although these results pinpoint some of the particularities of gravity with respect to other gauge theories, they do not constitute an impediment for the emergent gravity program if gauge symmetries (diffeomorphisms) are emergent in the sense discussed in this paper.